{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Coordinate Descent"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 主要讨论Coordinate Descent算法,并用来求解LASSO"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Coordinate Descent"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Alg**: <br/>\n",
    "$initialization\\ x = 0$ <br/>\n",
    "$repeat\\ for\\ k = 1,2,...: $\n",
    "$$\n",
    "\\begin{align}\n",
    "    x_{1}^{(k)}& \\in \\operatorname*{\\arg\\max}_{x_1} f(x_{1}, x_{2}^{(k-1)}, x_{3}^{(k-1)},...,x_{n}^{(k-1)}) \\\\\n",
    "    x_{2}^{(k)}& \\in \\operatorname*{\\arg\\max}_{x_2} f(x_{1}^{(k)}, x_{2}, x_{3}^{(k-1)},...,x_{n}^{(k-1)}) \\\\\n",
    "    &... \\\\\n",
    "    x_{n}^{(k)}& \\in \\operatorname*{\\arg\\max}_{x_n} f(x_{1}^{(k)}, x_{2}^{(k)}, x_{3}^{(k)},...,x_{n-1}^{(k)},x_{n})\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Lasso regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\begin{align}\n",
    "\\min_{w} E_{aug}(w)&=\\frac{1}{N}\\sum_{n=1}^{N}(w^{T}x_{n}-y_{n})^2 + \\frac{\\lambda}{N}\\sum_{q=0}^{Q}|w_q| \\\\\n",
    "\\frac{\\partial E_{aug}(w)}{\\partial w_{q}}&=\\frac{2}{N}\\sum_{n=1}^{N}(w^Tx_{n}-y_{n})x_{n,q} + \\frac{\\lambda}{N}\\partial|w_q| \\\\\n",
    "&=\\frac{2}{N}\\sum_{n=1}^{N}(w_qx_{n,q}^2 + \\sum_{p\\neq q}w_px_{p,n}x_{q,n}-y_{n}x_{q,n}) + \\frac{\\lambda}{N}\\partial|w_q| \\\\\n",
    "&=\\frac{2}{N}w_q\\sum_{n=1}^{N}x_{n,q}^2 + \\frac{2}{N}\\sum_{n=1}^{N}(\\sum_{p\\neq q}w_px_{p,n}x_{q,n}-y_{n}x_{q,n}) + \\frac{\\lambda}{N}\\partial|w_q| \\\\\n",
    "&=\\frac{2}{N}w_qX_q^{T}X_q + \\frac{2}{N}X_q^T(X_{-q}w_{-q}-y) + \\frac{\\lambda}{N}\\partial|w_q| \\\\\n",
    "\\text{又}\\quad &\\partial|w_q| =  \\begin{cases}\n",
    "                   1, &w_q > 0 \\\\\n",
    "                   [-1,1], &w_q = 0\\\\\n",
    "                   -1, &w_q < 0\\\\\n",
    "                   \\end{cases}\\\\\n",
    "\\text{从而有}\\quad&w_q =       \\begin{cases}\n",
    "                   \\frac{X_q^T(y-X_{-q} w_{-q}) - \\frac{\\lambda}{2}}{X_q^TX_q} & X_q^T(y-X_{-q} w_{-q}) > \\frac{\\lambda}{2} \\\\\n",
    "                   0 & X_q^T(y-X_{-q} w_{-q}) \\in [-\\frac{\\lambda}{2}, \\frac{\\lambda}{2}] \\\\\n",
    "                   \\frac{X_q^T(y-X_{-q} w_{-q}) + \\frac{\\lambda}{2}}{X_q^TX_q} & X_q^T(y-X_{-q} w_{-q}) < -\\frac{\\lambda}{2}\n",
    "                   \\end{cases}\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. 实现"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from sklearn import datasets\n",
    "from sklearn import linear_model\n",
    "%matplotlib inline\n",
    "plt.style.use('seaborn-white')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def lasso_reg(X, y, lambd=0.1, updates=1000, epsilon=1e-6):\n",
    "    w = np.zeros_like(X[0], dtype=np.float64)\n",
    "    w_last = w.copy()\n",
    "    \n",
    "    Xq_square = [X[:,i].dot(X[:,i]) for i in range(len(w))]\n",
    "    \n",
    "    for t in range(0, updates + 1):\n",
    "        if t % 100 == 0:\n",
    "            #print('\\repisode: ', t, end='')\n",
    "            pass\n",
    "            \n",
    "        for q in range(0, len(w)):\n",
    "            #index = [i for i in range(len(w)) if i!=q]     # 效率较低\n",
    "            #residual = y - X[:, index].dot(w[index])\n",
    "            \n",
    "            w_tmp = w.copy()\n",
    "            w_tmp[q] = 0\n",
    "            residual = y - X.dot(w_tmp)\n",
    "            \n",
    "            tmp = X[:, q].dot(residual)\n",
    "            if tmp > lambd/2:\n",
    "                w[q] = (tmp - lambd/2) / Xq_square[q]\n",
    "            elif tmp < -lambd/2:\n",
    "                w[q] = (tmp + lambd/2) / Xq_square[q]\n",
    "            else:\n",
    "                w[q] = 0.0\n",
    "        if np.linalg.norm(w_last-w) < epsilon:\n",
    "            break\n",
    "        w_last = w.copy()\n",
    "    return w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Lasso(alpha=0.1, copy_X=True, fit_intercept=False, max_iter=1000,\n",
       "   normalize=False, positive=False, precompute=False, random_state=None,\n",
       "   selection='cyclic', tol=0.0001, warm_start=False)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = np.array([[0, 0], [1, 1]])\n",
    "y = np.array([0,1])\n",
    "X = np.hstack((np.ones((2,1)), X))\n",
    "y = y - y.mean()\n",
    "reg = linear_model.Lasso(alpha=0.1, fit_intercept=False)\n",
    "reg.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.09997559  0.39997559  0.        ]\n"
     ]
    }
   ],
   "source": [
    "print(reg.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "[-9.99996185e-02  3.99999619e-01  5.55111512e-17]\n"
     ]
    }
   ],
   "source": [
    "w = lasso_reg(X,y,lambd=2*len(X)*.1)      # 主要是两者对目标函数的定义不同，故调整lambd\n",
    "print()\n",
    "print(w)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Lasso coefficient path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(442, 10)\n",
      "(442,)\n",
      "[[ 0.03807591  0.05068012  0.06169621  0.02187235 -0.0442235  -0.03482076\n",
      "  -0.04340085 -0.00259226  0.01990842 -0.01764613]\n",
      " [-0.00188202 -0.04464164 -0.05147406 -0.02632783 -0.00844872 -0.01916334\n",
      "   0.07441156 -0.03949338 -0.06832974 -0.09220405]]\n"
     ]
    }
   ],
   "source": [
    "#Load the diabetes dataset. In this case we will not be using a constant intercept feature\n",
    "diabetes = datasets.load_diabetes()\n",
    "X = diabetes.data\n",
    "y = diabetes.target\n",
    "print(X.shape)\n",
    "print(y.shape)\n",
    "print(X[:2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "alphas = np.logspace(-2,1,100)\n",
    "coefs_lib = []\n",
    "coefs_my = []\n",
    "\n",
    "for alpha in alphas:\n",
    "    reg = linear_model.Lasso(alpha=alpha, max_iter=1000, tol=1e-6, fit_intercept=False)\n",
    "    reg.fit(X, y)\n",
    "    coefs_lib.append(reg.coef_)\n",
    "    \n",
    "    coefs_my.append(lasso_reg(X,y,lambd=2*len(X)*alpha))\n",
    "    \n",
    "coefs_lib = np.array(coefs_lib)\n",
    "coefs_my = np.array(coefs_my)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.007079457843841388, 14.12537544622754, -354.439578670217, 616.684924792884)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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662hoaOD222/nL3/5C0OHDmXTpk3k5uaSkpLCsmXLsFgsPPXUUzz55JOkpqYyfvz4I65RwnQ7fbjtQyqbKzFrZqyaFatmxayZsagWEmwJWFUrVpO17ZhFs2DTbG2vrSZr22tN1QgSJBgMLQECoXUwQCAYIEgQf9BPMBhat+4PBAP7vD7QscZAgLrw/h+cG/ATDLZAoAUl2IIS9IbXLahBHyotqEEvGv7w2oepbfFjpgWT0oyFABbl+8V8CAE9EITmALiDCrUBcAcUmgMKzUFC6wA0hfc1BaA5qIRfh/Z7gz/sRFXUtmDdGrItmmWf12YtdNyiWtqOtf65ta73/rO0aN8vVs3atq/1z7S1j9ZjZi302qJa2vqUkC+EEEJ0DLvdzlNPPUVVVRWXX345gUCA888/n8LCQsaOHcuMGTOYOnUq11xzDVu2bIlo3xKm20FVVF674LVYl3HUCgRa8Psb8fka8fkb8Hrr8HrraPHV0uKtw+urx+urw+erw+erx+erx+9vIOBrwO9vIOhvJBho+tE+gpgIqHYCig2/asOHFa9ixYuFFsx4MOMOmnAHTTQFNJoCKk1BaPF7aQm00OhrpMZTgzfgpcXfQkughRZ/C97w8RZ/C0GCEfk8VEXFpJjagnzrYtEs+4R8i/p9OG89tk+gP8h2a7Bv/Y/A3vtsJts++6yaFZMqP+5CCCGi58KeFx7SKHI0FBYWoigKKSkpxMXFsX37dgoKCgCIj4+nZ8+ebdsejyeifcu/riJiVNWCqlowm5MOu41g0B8O2nV4vbWhta8Wn7cWr7cWr68mtO2rCb32VuP1luP11oRG2w9AUTVMlkQslmTM5mQslgwslhQs5hTMlpTQtiUVizkViyWVoGppm76zd+Buex3e1zrNp/V4i78Fb8DbtvgCvtC2/8Cv9w70rSG/tY29Q77H76ElcOD31h4mxbRP0LZqVuwme9tvTOyave03JzaTDbvJ/v1a2/f1/tsOkwOH2YFNs8n8eiGEEB1uzZo1AJSXl9PU1ERSUlKH/XskYVocVRRFw2xOxGxOxG4/9OuCwSB+fxNebw1eb1U4ZFfT4q3C21IV3q6kpaWKhoYNtLRU4fPVHrAtTXOEwrUlFYslHas1DaslncTwtsWRgc2agcmU2GE/qMFgEF/Ad8Bg3zpPv23e/l5z+Fvn7rv9bjx+zwFfu/1u3D43tZ5a3D43zb7mfY61h4ISCtdmR1vAdpgc2M12nCZn22un2XnAxWV2hdYWFy6zC6smd6sRQgjx09xuN9deey1NTU089NBD3HfffR3WtxIMRuZX2h1J1/UeQNGiRYvIycmJdTniGBUItIRCdktF2+LZa7vFUxZ+XYbPV/eD61XVjs2WFb61YWhts+dgt3fHYe+GxZJ+zAfBQDDQFsqbfc1tS5OvaZ/Xbfu9TW3Hm7xN36+9TTT6GvfZDgQDP9m/STW1Bex4S3xbyI6zxH2/mEPreGs88ZbQEmeJI8GagMPkOOb/DIQQQsRWSUlJ6y30cg3D2Lb/cRmZFsctVbVgtWZgtWb85Ll+v5uWljI8njI8LWV43KW4PbvxuHfj9uymofJzWlrKYa/51qpqw27vht3eDYe9Ow5HLnZHDxyOXKyWjGMi5KmKis0UmvaRSGLE2g0Gg7j9bhq9jT9YGrwNNLY0Uu+tp9HbSH3L9+v6lnp2NuykoaWB+pZ6GrwNPzrH3aSYvg/Z1lDI3ns6y95fCtYUDU3VQuvwtqqoaIqGSTWhKaHXrduaqmFSTG3ntW7bTDbizaH+XGaXfBFVCCE6OQnTQhwCTfs+GB9MINCC272L5uZimpuLaWreHt7eTlXV/wgEPHu15wiNYDtycTp64nDk4XT2wuHIRdPaMb/lGKUoStt861R76mG3EwgGaPCGgnWdpy60bqkLLZ46altq29a1nlpq3DWU+krbprm03vs9EnPSD6Z1JD3eEk+CNWGfdbw1tJ1gSSDRmkiCNbROtCVi1axRq0kIIUTkSJgWIkJU1YLD0QOHo8cPjgWDATyeUpqaikJL8zaamoqor1tLWdlCoHXKg4LN1gWnIw+nqw9OZ29czj44nb3QNEdHvp1jgqqobVM7uri6HHY7e99C0h/w4w/68Qf8+IK+tttK+gK+0P6gH1/A13auL+hru8YX8OH2uan3Hjjc17XUsa1uG7WeULj/sRBvN9lJsiaRaEskyZYU2raGtpNtySTZkkixpbRtu8yuY+K3HUII0dlImBaiAyiKis2Wjc2WTXLyqH2O+f0empu30dj0HY2N39HU9B2NjVuoLllCYK+wZbN1xeXqg8up43Ll43L1xeHojqLINIIjpSoqqqKGXnTgx+n2uanx1LSF6xpPTdvrak81tZ5aqtxV1Lhr2Fa7jRpPDY3eAz8l1aJa6Bbfjd5JvemT1IfeiaF1pjNTQrYQQkSRhGkhYkzTrLhcOi6Xvs/+QMCH272DhoZNNDZuoqFxE42Nm6ms/JRg+ImaqmrD5eyDy5VPXFwBcXEFuFz5x8VUkc7AZrKRacok05l5yNd4/B6q3dVUuava1lXuKiqaK9hWu43V5av5oOiDtvPjzHH0T+3PyOyRjMweSZ+kPt//x0EIIcQRkzAtxFFKVU04HLk4HLnA2W37/X4PTU1bqG/YQEODQUPDBsor/sOu3a0PFFJxOnsS5wqF67j4AcTHFcg0kU7CqlnJdP54AG9oaWBLzRY2VW9iU/Umlu9ZzqPLH4XlkGxL5sSsExmZPZKTsk8i3ZHegdULIUTnI2FaiGOMplnbRqFbBYNBPJ7d1NevCy0N66muWULpnrfDZ6g4nb2Ijz+B+PiBxMcPxOXUUVVzbN6EiCqXxcWg9EEMSh/Utm9P4x6W7F7CV7u/4qtdX7GgaAEA+cn5nNLlFE7NOZUBqQPk7iNCiGPOm2++ydatW/n1r38dk/4lTAvRCSiK0jYnOy1tTNt+T0sF9XVrqKtbRV39aioqPmb37teB0BSR+LgBJCQMISFhMAkJg7FYDv/OGuLoluHM4KJeF3FRr4sIBANsqt7Elzu/5POSz3l27bPMWTOHBGsCo7JHcWrOqZyScwrxlvhYly2EEEc9CdNCdGJWSyrW1DNITT0DCN/f2b2D2rpV1NWtorb2W4p3PEuw2AuA3d6NhIQhJCYOJylxOHZ7D/nyWiekKir5yfnkJ+dz44AbqfXU8tXur/hfyf/4YucXLChagEkxMTRzKGd2O5Mzup7RrnndQojjU83bb1P7rzcj2mbCzy8l8eKLf/K8lStXct1119HQ0MDtt9/OzJkzGTp0KJs3byYhIYFHH30UhyM60x0lTAtxHFEUpe1+2ZkZFwChB9LU16+ltvZbamu/pbLyc0pLQ9NDzOYUkhKHk5g4lMTE4bhc+Sjy5bVOJ8GawNgeYxnbYyyBYIDV5av5ZMcnfLLjEx7++mEe/vphClIKOLPbmYzpPobchNxYlyyEEPuw2+089dRTVFVVcfnllxMIBLjgggsYNmwYM2fOZP78+Vx//fVR6VvCtBDHOU2zhcPyUCA0et3UVERNzTfU1C6lpmYpZeWhu0OYzUkkJo4gOWkkSUkjcTjyZOS6k1EVtW2+9dTCqWyt3conxZ/w3x3/ZfaK2cxeMZs+SX04q/tZnN3jbHok9Ih1yUKIo0TixRcf0ihyNBQWFqIoCikpKcTFxVFfX8+wYcMAGDJkCJ9//nnU+pYwLYTYh6IoOJ15OJ15dOlyJQBu9y6qq7+mumYJ1VWLKS9fCIDFkk5y0kiSk08mOflkrFa5M0Rnk5eQR96APG4ccCN7GvfwcfHHfLjtQ55Y+QRPrHyCPkl9OLvH2ZyTew5d47rGulwhxHFqzZo1AJSXl9PU1EQwGGTjxo3k5+ezfPlyevXqFbW+lWAwGLXGo0XX9R5A0aJFi8jJyYl1OUIcV1rnXVdVf0V19VdUVS3G660EwOXKJzn5FFKSTyEhYSiaPBK70yptLOXj7R/z0faPWFG2AoAT0k7g/LzzObvH2STZkmJcoRDiePHmm2/y/vvv4/V6aWpq4le/+hX33XcfgwcPZteuXWRnZ/PHP/4Ri8VyWO2XlJQwevRogFzDMLbtf1zCtBDiiASDARoaNlBZ9QVVlZ9TU7ucYNCLqtpITjqJlNQzSE05A5stK9aliijZ3bCbBUULeG/re2yp2YJJMTGqyyjOzzuf07uejs1ki3WJQojjzJlnnskHH3yA1Xrkgzo/FaZlmocQ4ogoitp23+se3W/B52ukpuYbKis/o6LyEyoq/4sBuFz9SE09g9SUM4mPHyhfZOxEslxZ3DjgRm4ccCNGlcH7W9/n/aL3+azkM+IscZybey6X9L6Efsn9ZI69EKLTkZFpIUTUBIPB8CPQP6Gi4hNqapcDASyWdNLSfkZa2tkkJY6Qh8d0Qv6An6V7lvL2lrf5ePvHePwe+iT14dLel3Je7nkk2hJjXaIQQhwSmeYhhDhqeL01VFZ+Rnn5f6io/JRAoBmTKZ7UlDNJSzuLlJRT0TR7rMsUEVbXUscHWz/grS1vsa5yHWbVzM+6/Ywr8q9gSPoQGa0WQhzVJEwLIY5Kfr+bqqovKC//iPKKRfh8NWiag9SUM8nIOI/k5NPkC4ydkFFl8NaWt3hnyzvUe+vpldiLcfo4Lsi7AJfFFevyhBDiByRMCyGOeoGAj5qabygrW0BZ+Yd4vVVomou0tJ+RkX4+ycmjUNXD+xa2ODo1eZtYuG0h8435rK9cj91k5/y887ky/0r6JPWJdXlCCNFGwrQQ4pgSCPiorv6KPWXvU17+IT5fHWZzEhnp55OZdQnxcQNlWkAns7ZiLa9ufJWF2xbi8XsYkTWCa/tdy8ldTkaVL6oKIWJMwrQQ4pgVCLRQVfUFu0vfpqLiYwIBDw5HLpkZF5OZeTF2u/z8dya1nlpe3/Q6r2x8hbKmMnrE92BCvwlc0PMC7CaZSy+EOHTbt29nypQpvPfee0fcloRpIUSn4PPVU1b2AbtL36am5msAEhNHkJ09jvS0sWia3Mu4s/AGvHy07SPmrZ/Husp1JFgTGNdnHFf3vZoUe0qsyxNCHOXefvttXnjhBfbs2cOXX355xO1JmBZCdDrNzSWU7vk3u3e/QXNzMSZTPJmZF5GddQVxcX1jXZ6IkGAwyIqyFcxbP49FxYuwaBYu6XUJ1/e/nmxXdqzLE0LsZ+OS3Wz4cndE2+w7Kov8Ew/+0K+ioiJmzJiByWRC0zRmzpzJ+vXrGTFiBGPGjOmQMC0PbRFCHHPs9hxye0yhR/dfUF3zNbt2vcauXfMpKZlHXNwAumRfQUbGhZhMzliXKo6AoigMyRjCkIwhFNUW8dza53hj8xu8sekNzs07lxv630DPxJ6xLlMIEUOLFy+moKCA6dOns2zZMmpraznjjDM6tAYZmRZCdApebw2lpW+zc9d8Ghs3oWkusrMuIyfnGhyO3FiXJyKktLGUuevm8q/N/6LZ18zobqP5xQm/QE/WY12aECIGPB4Pc+bMYenSpcTFxTF16lR69gz9J3vUqFEdMjItX5MWQnQKZnMiXbtOZMTwBRQWvkZq6pmU7HyJr5b8jBUrJ1Je/jHBoD/WZYojlOnM5J7h9/Dhzz/kloG38M3ub7js3cu469O72Fy9OdblCSE62KJFiygsLGTu3LmMHTuWp59+usNrkJFpIUSn5fGUs2vXfHbuegWPpxSrNZOEhCG4XPnEufrhcuVjtWbKrfaOYXUtdcxbP4956+fR5G1ibI+xTB40mbyEvFiXJoToAMXFxUybNg1N01BVlRkzZlBQUAB03Mi0hGkhRKcXCHipqFhE6Z53aahfT7O7uO2YyZSIy6VjNsWjajZU1Yqq2tBUa2hbs6GpNlTVhqpZ27Y1zb7XMTuaFtqnaXGoqnwdpaPVemqZu24uL254EY/fw7m55zJl0BRy4uTfCCHEkZEvIAohjnuqaiY9fSzp6WOB0G32GhoM6hs20FC/nsbGzTQ1bycQ8Oyz+P1uINDe3rBZM7HZc7DZumC35WCz5WCzd8Fu64bNlomiaBF/j8e7BGsCdwy5gwn9JvDcuud4ZcMrLNy2kCv1K7l54M0k2ZJiXaIQopOSkWkhhDiIYDBIMOhtC9aBgBt/wE3A7w6w+Mt+AAAgAElEQVTvayYQaP7+mL+JFm81bncJ7uadNLtL8HhKge//nlUUMzZbNnZ7t/DSFYe9O3Z7D+z27miaNXZvuBMpayrj7yv/zltb3sJhcnDjgBu5uu/V8vAXIUS7yci0EEIcJkVRUBQLqmrBZIo7rDYCgRY8nlKam3eEFvcOmpuLaW4upq5uNT5f7d49YrNmYXd0x2HvgcORh8ORi8ORh92eIyPa7ZDuSOfBkx5kQr8JPPbtY/z127/yysZXmDJoChf1vAhNlc9SCBEZEqaFECKKVNXSNgp9IF5vLc3N22lq2kZT83aaw+uy8oV4vdVt5ymKBYejOw5HHk5HT5zO3jidvXE48mQ0+0f0TOzJ7DNns3zPch5d9ii/XfxbXtn4CjOGz2BIxpBYlyeE6AQkTAshRAyZzQmYzQOJjx/4g2NebzWNTVtpatxKU9NWGpu20ti4mYqKvW/zp2K3d8Xp7E2cqy/x8QOJixuA1ZrWsW/kKFeYUciL577Ih9s+5C/L/8J1C6/jnNxzuKvwLjKdmbEuTwhxDJMwLYQQRymzOYnEhEISEwr32R8ItNDUVERj45bQ0rSFhoZNVFT8l9YvTFqtmcTHDyQ+bgDxCYNJiB+Mptli8C6OHoqiMDZ3LKd1PY1n1z7Lc2uf49Mdn3Jj/xuZ2H8iVhnhF0IcBgnTQghxjFFVCy6Xjsu171P/fL5GGho2UFe3mrr6NdTVraa8/CMgNE0kIf4EEpOGk5Q4goSEwWiaIxblx5zdZGfKoClc3Oti/rLsLzyx8gne2vIWvx/1e4ZlDot1eUKII/TnP/+Zb7/9Fp/PxxVXXMG4ceOi2p+EaSGE6CRMJieJiUNJTBzats/rraO2djnVNV9TU/MN27c/ybZtf0NRTMTHn0By0iiSk0cRH38CqmqOYfUdr4urC4+e/ihf7/6aPyz5Azd/dDP3nngvl/e5PNalCSEO05IlSyguLmb+/Pm0tLRw3nnncfbZZ5OQkBC1PiVMCyFEJ2Y2x5OaegapqWcA4PM1hMJ19ddU1yyhaNsTFG17HE1zkpg4nOTkUSQnjcLp7H3cPBlyRNYIXj7vZe7+/G4e+uohtlRvYdqwaZjk4TtCtMu6zxax9tP/RLTN/qePoeC00Qc9XlRUxIwZMzCZTGiaxsyZM3n44Yfbjvv9fkym6P4sy98UQghxHDGZXKSknEZKymlA6G4i1TVLqKpaTHX1l2ze/AkQmnOdknwqKSmnk5x80mHfGvBYEWeJ44kzn2DW8lnMXT+XrbVbeeS0R0iwRm80Swhx5BYvXkxBQQHTp09n2bJl1NbWkpGRgdfrZfr06VxxxRU4nc6o1iAPbRFCCNHG7d5FZdX/qKz8jKqqL/H7G1AUEwkJhaSknEZq6pk4Hb069aj1W5vf4qElD9HF1YXHz3ycvIS8WJckhDgIj8fDnDlzWLp0KXFxcUydOpXU1FTuuOMOhg8fzpQpU464j596aIuEaSGEEAcUCHiprV1BZdVnVFZ+RkPDBgDs9u6kpf6M1NTRJCQUonbC6RArylZw5yd34vV7eeT0Rzgp+6RYlySEOIAFCxaQlJTEyJEjee+99/jyyy/ZuHEj119/PRdeeGFE+pAwLYQQIiLc7t1UVH5CRcXHVFV9RTDYgsmUQGrKGaSnn01y8qmd6vZ7uxp2cdt/b6OotoiZp85kTPcxsS5JCLGf4uJipk2bhqZpqKrKmWeeyd///nf69u3bds7DDz9M165dD7sPCdNCCCEizudroKrqC8orPqai4hN8vho0zUFKyumkp59DSvJpmEzRnafYEepa6pjy8RRWV6zmwZEPcknvS2JdkhCig/1UmO58v5sTQggRdSaTi/T0saSnjyUQ8FJT8w1l5QspK/uQsrIFqKqVlJTTyEg/j9TU0WiaPdYlH5Z4Szz/HPNPpn46lQcWP0CDt4EJ/SbEuiwhxFFEwrQQQogjoqrm0C31kkeh93mQmprllJV/QHnZh5SXf4SmOUlLHUNGxvkkJ598zN3P2mF2MPvM2Uz/33RmLp1JfUs9vzjhF536S5hCiEMnYVoIIUTEKIpGUtJwkpKG06f3/dTULKV0zzuUlS2kdM/bmM1JpKefS2bmRSTEDzlmAqlFszDz1Jk8uPhB/rHqH9S11HH3sLtRFTXWpQkhYkzCtBBCiKgIBesTSUo6Eb3Pg1RW/Y89pe+we/e/2LnzJRyOXLIyf05m5sXYbFmxLvcnmVQTD416iDhLHC9ueJFGbyMPjnwQTdViXZoQIoYkTAshhIg6VbWQljqatNTR+HwNlJUtZHfpv/hu6yN8t/UvJCefTFbmpaSlnXVU3xFEVVTuHnY3TrOTf67+JwC/O+l3MkItxHFMwrQQQogOZTK5yM6+jOzsy2hq2s7u0jcp3f0m69ZPxWRKICvrUrpkj8fp7BnrUg9IURRuG3wbiqLw5KonUVB48KQHJVALcZySMC2EECJmHI7u9MybSl7uL6mu/oqdu+ZTUvIiO3Y8R2LicLpkjyc9/WxU1RrrUn/g1hNuJRgM8s/V/0RRFH478rcSqIU4CsyaNYvFixejKAr3338/AwcOjGp/HR6mdV1PB5YDYwAf8DwQBNYCUwzDCOi6/lvgvPDxOw3D+Kaj6xRCCNFxFEVtuyNIS0tFeF71q6xbP5VNm5PJyvo5OV0mYLd3iXWpbRRFYcqgKQQJ8tTqp1BQeGDkAxKohYih9evXs3LlSl577TV27tzJrbfeyjvvvBPVPjs0TOu6bgb+CTSHdz0K3G8Yxqe6rj8JXKTr+nbgNGAE0BX4FzCsI+sUQggROxZLKt2730K3bjdRVb2YnTtfZseOZykufoa0tDF0zZlIYuKwo+JOIIqicNug2wgGg8xZMwdAArU4bjUu30Pjsj0RbdM5NANnYcZBjxcVFTFjxgxMJhOapjFz5kyeeeYZFEVh165dpKamRrSeA+nokelHgCeBGeHXhcBn4e0PgLMAA/jIMIwgUKzruknX9TTDMMo7uFYhhBAxpCgqKcknk5J8Mm73Lkp2vsTOna9SXv4hLlc/uuZcR0bGBWhabKeAKIrC7YNvJ0iQp9c8jaZo3H/i/UdF2Beis1u8eDEFBQVMnz6dZcuWUVtbS0ZGBrNmzeKFF17gN7/5TdRr6LAwrev6RKDcMIwPdV1vDdNKODQD1AMJQDxQudelrfslTAshxHHKZsumV89p5Pa4jdLSf7Oj5Hk2bLyHLd/9ma4515GTcw1mc2LM6lMUhTsG30EgGODZtc/isriYWjg1ZvUIEQvOwh8fRY6Gyy67jDlz5jBp0iTi4uKYOjX0czd16lRuuukmrrjiCoYOHUq3bt2iVkNH/h7qBmCMruufAoOAF4D0vY7HATVAXXh7//1CCCGOc5pmp0uXKxkx/AMGD3qB+PiBbC2axZeLT2HT5j/gdu+KWW2KonDnkDsZ12ccz659lmfXPhuzWoQ4XixatIjCwkLmzp3L2LFjuemmm/jd734HgNVqxWQyRf23RB02Mm0Yxqmt2+FAPRn4P13XTzcM41PgHOATYAswU9f1R4AcQDUMo6Kj6hRCCHH0UxSl7QuLDQ0G24ufoqRkHiUl88jIuIDu3W7C5dJjUte9I+6lvqWeWctnEW+J57I+l3V4HUIcL/r378+0adOYPXs2qqry+OOP8/rrr3PllVcSCAS4+uqr6dq1a1RriPWt8X4FzNF13QJsAN4wDMOv6/r/gK8IjZxPiWWBQgghjm4ul05Bv7/QM+9XFBc/w85d8yktfYu0tLPI7XE7cXH9OrQeTdX4fyf/P+q8dfx+ye+Jt8RzVo+zOrQGIY4X3bp1Y/78+fvs69+/f4fWoASDwZ8+6yij63oPoGjRokXk5OTEuhwhhBBHEa+3mh07XmBHyXP4fPWkpY4hN/d24uIKOrSOZl8zt/znFtZUrOFvo//GSdkndWj/QojIKCkpYfTo0QC5hmFs2/+43LtHCCFEp2I2J5GX90tOGvk5ubm/pLrma75ZeiGrVt9CXf3aDqvDbrLzxOgn6JnQkzs/uZNV5as6rG8hRMeRMC2EEKJTMpvjycu9g1EnfU5e7p3U1HzD0qUXsXrNrTQ2ftchNcRb4nlyzJOk2lO59eNb2Vq7tUP6FUJ0HAnTQgghOjWTKY7c3NsZdVJopLqq6guWfD2WDRtm4Hbvjnr/qfZUnhrzFCbVxK0f30plc+VPXySEOGZImBZCCHFcMJniyMu9g5NGfkLXrtexu/Rtvloyms1b/oTXG907sObE5fDEmU9Q2VzJHf+9A7fPHdX+hBAdR8K0EEKI44rFkkKf3vcz8sT/kJF+HsXFT7P4q9PZvfvNqPY7IG0AfzrlT6ypWMOM/80gEAxEtT8hRMeQMC2EEOK4ZLfn0K/f/zFi+Pu4XP1Yv2Eamzc/TCDgi1qfo7uPZtqwaXxc/DGPLns0av0Icbxrbm7moosu4vPPP496XxKmhRBCHNdcLp3Bg+aSk3MtxTueYdXqSXi9tVHr75q+13BV/lXMXT+XVze+GrV+hDiePfTQQ1F/8mGrWD+0RQghhIg5VTWj9/ktLqeOselBli3/OQMHPIXTmRfxvhRF4e5hd7OrYRd//OaPZLuyOTXn1J++UIij3MqVK1mxYkVE2xw8eDCDBg066PGioiJmzJiByWRC0zRmzpzJe++9x+DBg+moZ6nIyLQQQggR1qXLlQwePA+vt5Zlyy+lovLTqPSjqRp/PvXP5Cfn8+vPfs3WGrllnhCHY/HixRQUFPDcc88xefJkFi5cyPbt2xk3blyH1SBPQBRCCCH209y8k9VrbqGhwaBP7/vo2nViVPopayrj5+/8nBxXDvPOnYdJlV8YC9EeHo+HOXPmsHTpUuLi4gCoqKjAbDazdetWkpOTmTlzJn379j3sPuQJiEIIIUQ72e1dGFr4Gmmpo9m0+fdsLXo8Kr8yTnekc9+J97G2ci3Pr3s+4u0L0dktWrSIwsJC5s6dy9ixY4mLi+PVV19l3rx5nHLKKUybNu2IgvShkDAthBBCHICmOejf/wmyMi+lqOivbN7ycFQC9dgeYzmr+1n8beXf2FS9KeLtC9GZ9e/fn8cee4yrrrqKV199lWuuuabDa5BpHkIIIcSPCAYDbNr8e0pKXiA7axz5+X9AUbSI9lHtrubif19MhiODl857CbNqjmj7QojDJ9M8hBBCiCOgKCp9ej9Ajx5T2LX7Ndauu5NAoCWifSTZknjgxAfYULWBp1c/HdG2hRDRJWFaCCGE+AmKotAz7y569ZpOWdkCVq+ZjN/fHNE+RncfzXl55/HU6qdYX7k+om0LIaJHwrQQQghxiLp3u4l8/Q9UVn7OylU34vc3RbT9GcNnkGRL4v4v76fFH9nRbyFEdEiYFkIIIdqhS5fxFPR7lJqapaxadVNER6gTrAk8eNKDbK7ezJOrnoxYu0KI6JEwLYQQQrRTZuaFFPR7hOqab1i1OrKB+tScU7m418U8s/YZ1lWsi1i7QojokDAthBBCHIbMzIvo13cm1dVLWL36Fvx+d8TavnvY3STbknn4m+jcjk8IETkSpoUQQojDlJV1Cf36/pmq6sURDdRxljh+OeSXrC5fzXtb34tIm0IcLyZPnsyVV17JhAkTmDRpUtT7k+eWCiGEEEcgK+vnBINBNmyczuo1kxk44J9omvWI272w54XM3zifx5Y/xuhuo3GYHRGoVojOr7i4mPfffx9FUTqkPwnTQgghxBHKzr4MCLBh4wzWrL2VgQP+gapajqhNVVG5Z/g9TPhgAk+veZo7htwRmWKFiJLdu99k1+43ItpmdtZlZGVdetDjRUVFzJgxA5PJhKZpPPzww9TV1TF58mTq6uq4+eabOeOMMyJa0/4kTAshhBARkJ09jmDQz0bjftavn0ZBwaNH/KTEQemDOD/vfOaum8slvS+ha1zXCFUrROewePFiCgoKmD59OsuWLWP37t3ccMMNXHvttdTW1jJ+/HgGDhxISkpK1GqQMC2EEEJESJcu4/H66vjuu5mYzAnofX53xL9qvnPInSwqXsRflv2Fx854LEKVChF5WVmX/ugocjRcdtllzJkzh0mTJhEXF8ftt9/OlVdeiclkIiUlhb59+1JUVBTVMC1fQBRCCCEiqEf3W+jW7SZ27nyJrUWzjri9DGcGNw24iUXFi1iye0kEKhSi81i0aBGFhYXMnTuXsWPH8otf/II777wTgMbGRjZv3kxeXl5Ua5CRaSGEECLCevW8B5+3lm3b/obZnES3rtcfUXvXFlzLvzb/iz9/82dev+B1TKr88y0EQP/+/Zk2bRqzZ89GVVVmz57N22+/zbhx41BVlbvuuovk5OSo1iA/jUIIIUSEKYqCrv8er6+GzZv/gNmUcES//rZqVqYNncadn97J65teZ3z++AhWK8Sxq1u3bsyfP3+ffQUFBR1ag0zzEEIIIaJAVU0U9HuMpKSRbNg4nfLyj4+ovTO7ncmIzBE8seIJatw1EapSCHGkJEwLIYQQUaJpVgYOeJI4VwFr191Obe23h92WoijcPfxuGrwNPLn6yQhWKYQ4EhKmhRBCiCgymVyccMIzWK2ZrFp9C83NxYfdVp+kPlzS6xLmG/PZUb8jglUKIQ6XhGkhhBAiyiyWZAad8CzBYICVq27E6z38aRq3DroVk2Ji9orZEaxQCHG45AuI7RAMBNhx8y34qipR7Q5Uuz20OOwoDgeqwxHa37rtbN1nR7HZUe02FJsN1RZe2+0oFguKKv+nEUKIzs7hyGXgwCdZseJaVq+5lcGDnkNV2//Y8XRHOhP6TWDOmjlMLJhIv5R+UahWCHGoJEy3k7VXL5QijUBzM/7aWryluwk2NRNoDi1Bt7vdbSoWSyhcW63hsG0Nhe/wa8VmRbXZ29aq3Y5it4W3bW1BPbTf/n3It38f8hWLpcOeUS+EEOLAkhKH0a/vn1i3/i42bLyXfn0fOay/m6/vfz2vb3qdWctnMeesOVGoVAhxqCRMt4OiqmRMv+dHzwn6/aFg3dhEoKmRQGMTQY+bQLOboLuZQLObgLuZYLObgNtN0O0m2OIh4PaEznN7CLrdBDxugm4P/ro6gmXhc5ubCXg8BJubCXq97SteVb8fMbfbUZwONIcTpXX03OlsW2tOZ+i1yxXeH9rWXOF9cXESzoUQ4jBlZl5Ec3MxW4sew27vTl7uHe1uI84Sx80Db2bm0pks3rWYk7JPikKlQhyb3nzzTV555RX8fj+jR49mypQpUe1PwnSEKZqG5nKhuVxR7Sfo84WDd3hUvKl5n+1Ac1MofLeOmjc1EWhuItDURLCpKbS/sRF/RSXexuLQ8cZGAk1NEAz+dAFmcyh0h8O1FhcXWre+jo9DjYsPrePj0fbeTkhAdbkkjAshjls9etxGc3MxRUV/xW7rSlbWJe1u4wr9Cl7a8BKPLX+ME7NORFVkyqAQxcXFvPLKK8ybNw+LxcLjjz+O1+vFbDZHrU8J08coxWRCc5nA5Yxou8FgkGBTE/7GxlC4bgyH7MYGAg0N+BsaCDQ0EmhofV1PoL4Bf30d3pISPPX1oXPq6388lKsqWnw8akI8WkIiWkJCaElM/H7duiQlYUoKrVWHI6LvVwghYkFRFPLz/x9u9y42bJyB09mT+PiB7WrDolm4bfBtzPjfDD4o+oDz8s6LUrVCHJrXSqt4ZXdlRNscn5XCuMyDP8GwqKiIGTNmYDKZ0DSNYcOG0b9/f+655x7Ky8uZPHlyVIM0SJgW+1EUBSU8zeNIBAOBUAivq8NfV4e/rp5AfR3+2vDr2prQsZra0Ovqalq2bcNfUxMK4gerz2ZDS0pCS0rElJiElpKCKTkZLTkZU0oyWnIKpuQktNRUTCkpqHb7Eb0PIYSIFlW1MGDA3/n6m3NZv+Fuhg/7d7u/kHhu7rk8v/Z5Zq+YzZjuY7BolihVK8TRafHixRQUFDB9+nSWLVvG8uXLWbZsGa+88goej4fx48fzxhtvEB8fH7UaJEyLqFBUFS08/cPcpUu7rg36fKGAXVPz/VJdjb+6Gl91Nf7qGvxVVaEAvmMH/srK0PSUA1CdTrTUFEwpoXBtSkvDlJ4WWqemhtZpaWgpKXJXFSFEhzObE+ib/zArV93A1q1/pVevu9t1vaqoTC2cyuSPJ/Oa8RrX9LsmSpUK8dPGZSb/6ChyNFx22WXMmTOHSZMmERcXx6hRoxg+fDgulwuXy0XPnj3Ztm0bAwe27zc/7SFhWhx1FJMJU3IypuRD/4EMuN34q6rwVVbhr6rEV1GJr6ICX2UF/vC257vvaPz6awJ1dT9swGQKheuMdMzpGZjS0zFlZGDOzMCUmYk5KwtTRgaqRUZ9hBCRlZJyGtlZ49hePIe0tDEkJAxu1/UnZZ/EiKwR/HP1P7mo10XEWeKiVKkQR59FixZRWFjIbbfdxnvvvcf8+fOpqanB4/Hg9/v57rvv6NatW1RrkDAtOgXVZkPNzsacnf2T5wbc7lDYLi/DV14eWvaU4Ssrw1e2B8/WrTQuWXLA6SZaSgrmjAxMWVmhdWvgzsgMrdPTZV63EKLdeve+l6qqL8LTPd5F02yHfK2iKEwdMpUr37+S59c9z+2Db49ipUIcXfr378+0adOYPXs2qqoyY8YMli5dyvjx4wkGg9x6660kJiZGtQYleCh3bjjK6LreAyhatGgROTk5sS5HdFKBxka8e8rwle7GW7oHb+lufK3rPWX4Skvx19b+4DrV6QxPJ0lvm0YSGulObwvgpvR0VGv7H9YghOi8qqq+ZMXKa+nW9UZ697633df/6tNf8cXOL1j484Uk2ZKiUKEQx6eSkhJGjx4NkGsYxrb9j8vItBAHoTqdWPNyseblHvScQHMzvj17vg/bZeXfj3aXl9O8ejW+8vIDPsxHS0wMj2xnYsrKxJyZhTkrE1N4bc7MRJFpJUIcN5KTR9Gly9UU73iWtLSzSEwc2q7rf3HCL/jP9v8wd91c7iy8M0pVCiH2J2FaiCOg2u1YevTA0qPHQc8JBoME6utDoXtPGb49e/CV7cG7Z094pLuU5pUrfzjKrSiY0tIwh6evmLuE1zk5oaVLF5nDLUQn06vnPVRWfs76DdMYMfx9NO3Qp431SurF2B5jeXnjy1xbcC3Jto79IpgQxysJ00JEmaIoaPHxaPHxWHv3Puh5gaYmvKV7QtNKdpfi3bWrbWles4a6//wH9n7ypaJgSk/HnJODJScHc7euWLp1x9K9G+auXdESE+XBOEIcY0wmJ/36/plvV1zFlu/+D73Pb9t1/eQTJrNw20KeX/c8dxXeFaUqhRB7kzAtxFFCdTh+dFpJ0O/HV1GBt6SElh078JbsDG2X7KBxyRJ8//73vu3Fx2Pp1g1L9+6h0fPc3LZRdC3CD/sRQkROUtIIuuZMZEfJ86SnnUNS0vBDvjYvMY9zcs/h1Y2vcl2/60ixp0SxUiEESJgW4pihaBrmjAzMGRk4Cgt/cDzgdofCdXExLduL8e4IrZtXraJuwYJ9nkhpSksLheueeVjzemLtmYelZ09M6ekymi3EUaBnz19TXvEfNm1+iOHD/o2iaId87d6j078a+qsoVimEAAnTQnQaqs2GtVcvrL16/eBYwOPBW1yMZ9s2Woq20VJUREtREXXvL9jnvtuq04mlV0+svXtj690ba3jRUlMlZAvRgTTNTq9eM1i79jZ27ppPTperDvna3IRczs09NzQ6XXAdqfbUKFYqhJAwLcRxQLVa24Lx3oLBIP6KCjzfbcWz9TtavtuKZ8sWGv77CbVv/KvtPC0xMXR9fj62fB1rfj7WXr3k9n5CRFF62lgSE0ewdeujZKSfh9mccMjX3jLwFhYULeC5tc8xbdi0KFYphJAwLcRxTAnfMcSUlobzxBH7HPNVVuLZvAXP5s2hxTCoeeMNgs3NoRM0LTTHO78vtn79sBX0w9avH5rLFYN3IkTnoygKfXr/hm+WXkhR0eP06fObQ762R0IPzs87n9eM17i+//UyOi1EFEmYFkIckCklBVNKyj4hO+j301JcjMcwcG/ciGejQdM331D37rtt51i6d8dWUBAK1wMGYC8o4P+zd99hUpV3G8e/Z/rO9t57OUvvCEpRKUJoYkFUjKgxtmhMMcZEE42mGPOq0YgaCyoqICiKIAoSUUBBUEDqge2VXbb3MuX9Y1dslFWZPbO7v891zTXtOeG+MMzee+Y5z2PwlQsehfgh/P37ERs7n6LiJcTEzsfP9+QrAn3bDYNvYG3OWp7b+xx3jr7TgymF6NukTAshukwxGrEmJ2NNTiZg2rTjrzsqK2nZv5+WAwdo2b+fpt27Oi56BDAYsKalYRs8CJ9Bg/EZPAhrejqKST5+hOiKlOTbKStbw5HDDzB06Atdvn4hISCBmSkzWXF4BdcOvJZwe7iHkwrRN8lPMyHEj2YKDcVvwgT8Jkw4/pqjqoqWvXtp/mIvzXu/oOH9jcfnYSt2Oz6DB+MzbCj2YcPwGTIEY2DX54MK0ZdYLKEkJ9/GkSMPUFGxkfDwyV0+9obBN7AmZw3P7XuO34/+vQdTCtF3SZkWQniEKSQEv4kT8Zs4Eei42LG9sJDmPV/QvHs3zbt2UfnfZ6h0OgGwpKViHzES+8iR2EePwhwZqWd8IbxKXOwCiouXcSTrr4SGjsdg6NrFv/EB8cxKncXKwyu5ftD1su60EB4gZVoI0S0URenYRCYhgcBZMwFwNTbSvHcfzbt30fT559StXUvN8uUAmOPjsY8a1VmuR2OJi9UzvhC6MhjMZKTfze49CyksfIHExBu6fOy1A6/lray3eOXgK9w2/DYPphSib5IyLYTQjcHXF98xZx2/yNHtdNJy6BDNO3fSuGMHDRs3UvvGG0BHufYdMwbfsWOwn3UWplA5wyb6ltDQ8YSFTSY37wmiouZitUZ06bjkwGQmJ05m2aFlXDvwWvwssuKOEGeSlGkhhNdQjEZ8BpUW828AACAASURBVAzAZ8AAQq6+GrfLRWtWFk3bP6Vx2zbq3n2XmhUrALBmZOA7diy+48djHzVS1rwWfUJ62l1s2z6NnJxH6Nfv710+7rqB17EhfwMrDq/gmoHXeDChEH2PlGkhhNdSDAZsGRnYMjIIuWoBboeDlgMHaPxkG43bPqF66VKqXnwRxWbDPmoUfuPH4TtuPJbkJNmxUfRKdnsScXELKCx8kfiEa7u8VN6AsAGMiR7DSwde4op+V2A1yi+fQpwpBr0DCCFEVykmEz6DBxN2w89JXLyYjO3biP/v0wRdeinthYWU/e3v5PzkJ2RPnsLR+x+gYctWXG1tescW4oxKSrwZo9FOdva/vtdx1w26jormClZnr/ZQMiH6JjkzLYTosQw+Pt9Ykq+tqIjGLVto+PAjal5/nepXXsFgt+M7bhx+552H38QJmEJCdE4txI9jsYSQlHgD2Tn/R03NToKCRnbpuLOizmJg6EAW71vM3LS5mAxSAYQ4E+TMtBCi17DExRE8fz7xTy4i45OPiXtyEQGzZtG8ezeld93FkXHjyb/qp1S9/ArtZWV6xxXiB4uPX4jFEkFW9oO43e4uHaMoCtcNuo7C+kLez3/fwwmF6DukTAsheiWDjw/+551H9H33kvbhJpJeX0nYjTfirKmm7IEHyJp4LnnzL6dy8Qu0FRXrHVeI78VotJOS/Etqaz+nomJDl487P+F8kgKSeHbvs10u4UKIU5MyLYTo9RRFwWfAAMJvu5WUt98m5Z21hN/+S1ytrZQ/+CDZkyeTd9l8qpa8jKOiQu+4QnRJdPQl2O0pZGX/C5fL0aVjDIqBawdei1atsbVkq4cTCtE3SJkWQvQ51pQUwm68kZRVb5C6/j3Cf/NrXK2tlP31rxyZMJGC635Gzao3cTY06B1ViJMyGEykpv6WpqZsSktXdvm4mSkzibRH8tze5zyYToi+Q8q0EKJPsyQkEHb99aS8uYqUt1cT+vPracvP75hjfc44in/9axo2b8Hdue25EN4kPGwqgQHDyMn9N05nc5eOMRvNXD3ganaW7WR3+W4PJxSi95MyLYQQnazp6UTcfjupG9aTtGwpQRdfTOPWjym8/nqyzp9E+cOP0Jqbq3dMIY5TFIW0tN/T1lZOYeHiLh93cfrFBFoD5ey0EGeAlGkhhPgWRVHwGTqUqD/dQ9rmj4h99FFsmZlUPvssOdN/Qt7lV1Dz+uu4mpr0jioEQUEjCQubTF7+07S1VXXpGLvZzuWZl7OpaBO5tfILohA/hpRpIYQ4BYPFQsC0C4h/+inSNn1AxB134Kyro/SPd3NkwkSO3v8ALYcP6x1T9HGpKb/B6WwiL//JLh9zmXoZZoOZVw6+4sFkQvR+UqaFEKKLzBERhF53LSlr3ibxlZfxO/88alasIHf2HPIuv4Lat97C1dKid0zRB/n5ZRAddSHFxa/Q2lrepWPCfML4SfJPWJ29mtrWWg8nFKL3kjIthBDfk6Io2EeMIPaf/yTtw01E3HknzupqSu78PVmTJlP57LM4Gxr1jin6mKSkX+B2O8jLf6rLx1zV/yqaHc28fuR1DyYToneTMi2EED+CKTiY0GsWkrLuHRJeWIwtM5Pyf/0fWZMmceyJJ3DWyhk/0T3s9kSioi6ipGQpLa1Hu3SMGqIyOmo0rx58lXZXu4cTCtE7SZkWQogzQFEUfMeMIeG5Z0l6bTn2ESOoePw/x1cBcVR17cIwIX6M5KRbcLtd5H+Ps9ML+i2grKmMjQUbPZhMiN5LyrQQQpxhPoMHE7/oCZLfXIXv+PFUPvMMWZOnUP7Io3KmWniUj0880VEXUVy8nJaW0i4dMyFuAvH+8bx84GUPpxOid5IyLYQQHmLLzCTu0UdIWfM2/udOpPLpp8maMpWKp57C1ShzqoVnJCXdAri6PHfaaDByZb8r2XNsD18c+8Kz4YTohaRMCyGEh1lTU4l9+GGS31yFfcQIjj36b7KmTKXyhRdwtbbqHU/0Mj4+cURHX0JJyWu0tJR06ZgL0y7Ez+wnZ6eF+AGkTAshRDexZWYS/+QikpYtxapmUP6PB8m+YBo1q97E7XLpHU/0IslJtwDuLq877Wv25aL0i1ifv56jjV27eFEI0UHKtBBCdDOfoUNJXLyYhBdewBQeTuldd5F7ySU0btuudzTRS9hsMcTEXEpJyQqam4u7dMwV/a7AjZulh5Z6OJ0QvYuUaSGE0InvmLNIWr6MmIcewllTQ8HChRTeeBOtOTl6RxO9QFLiTYBCXv6iLo2P9YtlUsIkVh5eSVN7k2fDCdGLSJkWQggdKQYDgbNmkrpuHeG/+TVNO3eSM2s2R//yFxzV1XrHEz1Yx9npeZSWrqS5uahLxyzot4C6tjrW5KzxcDoheg8p00II4QUMVith119P6vr3CL7sMqqXv0bOtOlUL1uO2+nUO57ooZISb0RRDOTlPdGl8cMihtE/tD9LDizB5ZZ5/EJ0hZRpIYTwIqaQEKL+dA/Jq97Amp7O0XvvJW/eZTTv2aN3NNED2WzRxERfRunRVV1ad1pRFBb0W0BeXR7bSrd1Q0Ihej4p00II4YVsGRkkLHmJmIcewlFeTt5l8ym5+27ZSVF8bwkJPwNcFBQ+36XxU5OmEmQNYoW2wrPBhOglTN31B6mqagaeB5IAK/AAcAB4AXAD+4BbNE1zqar6Z2AG4ABu1zTt0+7KKYQQ3kJRFAJnzcTvvHOpeGIRVUuWUL/hfSJ++xuCLrkERVH0jih6AB+fOCIjZ1FSsozkpJsxm4NPOd5qtDI3bS4vHXiJssYyIn0juympED1Td56ZXgBUapo2HpgO/Ad4GLi78zUFmKOq6nBgInAWMB/o2kQvIYTopYx+fkTe+TtS3lyFLSODo/f8iYKrF9KWl6d3NNFDJCb8HKezicKiJV0af2nGpTjdTt448oaHkwnR83VnmV4B3PO15w5gBPBh5/N1wGRgHLBe0zS3pmkFgElV1fBuzCmEEF7JmpZGwosvEHX/X2g5eJCc2XOo+O8zuNvb9Y4mvJyfn0pY2CQKC1/E6Tz9snfxAfGcHXM2K4+sxOFydENCIXqubivTmqY1aJpWr6qqP7ASuBtQNE1zdw6pBwKBAKD2a4d++boQQvR5isFA8KWXkrJ2DX7nnsuxhx8m99J5NO/dp3c04eWSEm/E4aihuGR5l8bPU+dR3lTOh0Ufnn6wEH1Yt16AqKpqPPABsETTtFeBr6+74w/UAHWdj7/9uhBCiE7miAjiHvs3sY8/hrOykrzLLqP0vvtwHDumdzThpQIDhxMUNJqCgmdxudpOO35i3EQi7BG8pr3WDemE6Lm6rUyrqhoJrAfu1DTty0uKd6mqem7n4+nAZmArcIGqqgZVVRMAg6ZpFd2VUwghepKAKVNIWbuG4PnzqVmxkqypF1D+6KM46+v1jia8UFLijbS2HuVo2erTjjUZTFySfgkfl3xMQV1BN6QTomfqzjPTfwCCgXtUVd2kquomOqZ63Keq6ieABVipadpndJTqT4DXgVu6MaMQQvQ4xoAAov50D6lr1+B/3nlUPvU02ZOnUPn8YlytrXrHE14kJGQCfn79yM//L+4ubMpyUfpFGBUjKw+v7IZ0QvRMitvtPv0oL6OqahKQu3HjRuLi4vSOI4QQXqV5/36OPfIojVu2YIqOJuzn1xM4Zw4Gu13vaMILHC17m/37b2fQoEVEhF9w2vG/+uBX7CzbyfuXvo/VaO2GhEJ4l6KiIiZNmgSQrGla3rffl01bhBCil/EZMICEZ58h4YUXMEWEc/S+v3Bk4rmU/eNB2goL9Y4ndBYRPh0fnwTy856iKyfULlUvpaa1hvV567shnRA9j5RpIYTopXzHnEXSsmUkLn0Vv/HjqXr5ZbKnXkDhTTfTsHVrl4qU6H0MBhMJCddTV/8F1dWfnHb8mOgxJPgnyIWIQpyElGkhhOjFFEXBPmwYsQ//H2kbNxJ2040079lD4XU/I2fWLGpefwNX2+lXdhC9S3TUxVgs4eTnP3XasQbFwDx1HruP7Uar0rohnRA9y/cu06qqSgEXQogeyBwZQfhtt5G26QOi//F3FKOJ0j/+seNixWeflRVA+hCj0Up8/DVUVW+lvuHQacfPSZ2DxWBhxeEV3ZBOiJ6lS8VYVdVLVVWdr6rq1cBRVVV/6+FcQgghPMRgsRB04YUkv7mK+GefxZKaQvm//o+sc8+j7J8P0V5WpndE0Q1iYy7DYPChsHDxaccG2YK4IOkC3s5+m8b2xm5IJ0TP0dWzzL8FNgALgHhglscSCSGE6BaKouA37hwSFy8m6fWV+E2cSNULL5A9eQql995Le3Gx3hGFB5nNQURHX8TRo6tpazv9dg7z1Hk0OZp4N/fdbkgnRM/R1TL95UKl9ZqmtfLNHQqFEEL0cD4DBhD78P+Ruv49Ai++iJrX3yDrgmmU3nOPrADSi8XHLcTtbqOoeOlpxw4JH0JyYDJvZr3ZDcmE6Dm6WqZzgJ3A86qq/hnY7rlIQggh9GKJiyP63ntJW/8ewZddRu1bq8meNp2Su/5AW16e3vHEGebrm0Jo6LkUF7+My3XqDX4URWFu2lx2H9tNTm1ONyUUwvt1tUzfDQzSNG0N8DTwqOciCSGE0Js5Opqoe+4mdcMGQhZcSd0775A9YyYld99Ne2mp3vHEGRQffw1tbRWUla057dhZqbMwKkbeynqrG5IJ0TOcskyrqjpQVdULgDXA2aqqTgWGAcu7I5wQQgh9mSMjiLzrLtLe30DwlVdQ99Zqsi+YRtnf/4GjqkrveOIMCAk+B1/fdAoKXzjt2uNhPmGMjx3P6uzVOFyObkoohHc73ZnpYGA+EAlc3nm7BFjk4VxCCCG8iCk8nKg//IHUd9cRMHMmVUuWkD15Csce/w/Ohga944kfQVEU4uMW0tBwgJqaT087/sL0C6lormBr8dZuSCeE9ztlmdY0bbOmadcAMzRNu6bzdp2maf/tpnxCCCG8iDk2lpi//ZWUt1fjO24cFU88QfaUqVS9/Aru9na944kfKCrqQszmYAoKnz/t2AlxEwixhciFiEJ06uqc6VBVVd9RVfV/X948mkoIIYRXs6amEvfYv0lasQJrRgZlDzxAzoVzafjwQ9mmvAcyGm3ExlxORcVGmpryTznWbDAzM2Ummwo3UdUiU32E6GqZfgR4GLjpazchhBB9nM+ggSS8sJi4RU+Aw0HhDTdS+LPraTl8WO9o4nuKi1uAopgoKnrptGMvTLsQh9vB2py13ZBMCO/W1TJdoGna+9rXeDSVEEKIHkNRFPzPP5+Ut1cTedfvad67l9wL51J67704qqv1jie6yGqNJDJiBiWlK3E4Tr21fHpwOgNDB7Iqa5V8EyH6vK6W6XJVVZ9SVfUGVVV/rqrqzz2aSgghRI+jWCyEXH01qe+9S/AVV1CzYiU506ZTvfw13C6X3vFEF8THL8TpbKCkZMVpx85Nn8uR6iMcqDzQDcmE8F5dLdO5QCkQBUR33oQQQojvMAUHE3X3H0l5cxXWjAyO/vnP5M2/nOZ9+/WOJk4jIGAQgYEjKSx6Ebfbecqx05KnYTVaWZW1qpvSCeGdulSmNU27D9gKlACrgAc9GUoIIUTPZ01PJ+GlF4l56J+0l5SQd+mlHP3L/Tjr6vSOJk4hPn4hLS1FVFRuOuW4AEsAkxIm8U7uO7Q6T717ohC9WZfKtKqqfwN+Cvycjk1bFnsylBBCiN5BURQCZ80i9Z21BF95JdXLlpE9/SfUvr1G5tp6qfCwyVgsERQXv3rasXPT51LfVs//CmSRL9F3dXWaxzhN034KNGia9iKQ7MFMQgghehljQABRd/+R5JUrMMfGUnLHHRTdeJNsTe6FDAYzMTHzqKz8kObmwlOOHR01mhjfGFYdkakeou/qapk2qapqA9yqqhqBU0+kEkIIIU7A1r8/SUtfJeL3d9K4fTs5M2dRvWy5XKDoZWJjLgMUikuWnXKcQTFwYdqFbCvdRmmD/GIk+qbvs870Z8BAYDuynbgQQogfSDEaCV24kJS3V2MbNIij995LwcJraMs/9WYhovvYbDGEhZ1PSclruFynng89O202bty8nfN2N6UTwrt09QLEFcA4YAYwTdO0VzyaSgghRK9niY8nYfHzRN3/F1oOHCBn9hwqF78gZ6m9RFzsFbS3V1F+bP0px8X6xTI8Yjhrc9bKPHjRJ52yTKuqenfn/VLgCeBXwGOqqp7+qgQhhBDiNBRFIfjSS0lZuwbfsWMpf/BBCq65VuZSe4GQkPH42BK6dCHijJQZ5NTmcKjqUDckE8K7nO7M9Jff2TwFPP2tmxBCCHFGmCMjiXtyEVH3/4XmvXvJmT2H2rfX6B2rT1MUA7Gx86mp+ZSGhlNvD39B0gWYDCbZXlz0Sacs05qm7el8GABM0jTtQ+AuwObpYEIIIfqW42ep31yFNTWVkjvuoPjXv8FZW6t3tD4rOvoSFMVCccnSU44LtAYyLnYc63LX4XTJGgWib+nqBYj3Af/pfHwZ8GfPxBFCCNHXWRISSHx5CeG3/5K69evJmT2Hxk8+0TtWn2SxhBIRMY3S0jdwOptOOXZGygzKm8vZUbajm9IJ4R26WqbbNU0rB9A0rRZZGk8IIYQHKSYTYTfeSNKyZRh8fSm49jrKH30Ut8Ohd7Q+Jy72SpzOBo6WnXq1jnPjzsXX7CtTPUSf09Uy/amqqq+qqnqrqqpLgF2eDCWEEEIA+AwcQPLrKwm8aC6VTz1NwcJraC8r1ztWnxIYOAJf33SKi1855WodNpONSQmTeD//fdleXPQpXS3TtwGvAXbgNU3TbvNcJCGEEOIrBh8fYv76V2Ie/AfN+/eTO3cuDZu36B2rz1AUhdjYK6mv3099/d5Tjp2ZMpOG9gY+LPywm9IJob/TLY03s/Ph9UAEUA1Eq6r6c08H80ZOp5PHH3+c5557ji1btlBeXi5ragohRDcJnDOH5JUrMIWGUnj99ZQ/ItM+ukt01IUYjXaKik+9zcToqNGE+4TLVA/Rp5zuzHRq5330CW59jsFgYOTIkbS3t/P++++zaNEiHnvsMdatW0d2djZOp0wlF0IIT7KmppL02nKCLr2EyqefJn/hQhzHjukdq9czmfyJjJxFWdnbtLeffHUVo8HItORpbC7eTG2rrMIi+gbTad6/GPg3EKVp2k3dkMerKYrC2LFjGTt2LLW1tRw+fJjDhw+zc+dOtm/fjs1mQ1VV+vXrR2pqKmazWe/IQgjR6xh8fIi+/37so0ZR+qc/k3vJpcQ9/hg+gwfrHa1Xi429gpKS5RwtW0183FUnHTcjZQZLDixhQ/4GLsm4pBsTCqEP5VTTFFRVfRcIBdKBA19/T9O0sz0b7eRUVU0Ccjdu3EhcXJxeMY5ra2sjJyeHgwcPomkaLS0tmM1m0tPT6devHxkZGVitVr1jCiFEr9Ny6BBFt/wCR3k5UffeS9DFF+kdqVfb/ulMFMXA6FGrTzrG7XYz+83ZhPmEsXja4m5MJ4RnFBUVMWnSJIBkTdPyvv3+6c5M/wqop2PHw5vPeLpewmKxkJmZSWZmJk6nk7y8PA4cOMChQ4c4cOAAJpOJjIwMBg4cSHp6upyxFkKIM8SWmUnSyhUU//rXlP7xj7Ts30/kXb9Hkc9Zj4iJvoTDR+6nvv4g/v79TjhGURRmpMzgid1PcLTxKFG+Ud2cUojudboy/ZymaWerqtqmaVp+tyTq4YxGI6mpqaSmpjJjxgwKCwvZt28f+/fv58CBA1itVjIzMxk0aBDJyckYjUa9IwshRI9mCg4m4ZlnKH/4Eaqef57Ww4eJ/fejmEJD9Y7W60RFzeFI1oOUlq7E3/+ek46bkdxRpt/JfYdrB17bjQmF6H6nm+bxEjAVCAKqAKXzLbemaTGej3fSXEl40TSPrnA6neTm5rJv3z4OHjxIa2srFouF2NhY4uPjiYuLIy4uDrvdrndUIYTosWrfXkPpPfdgDAoi/qknsWVm6h2p19m771aqqz9h3DkfYzBYTjruyneupNnRzBuz3+jGdEKceT9qmoemaT8FUFX1CU3TbvFIwj7CaDSSlpZGWloaM2bMICsri5ycHAoLC9m8efPxJfZCQ0OJi4sjPj6e+Ph4wsPDMRi6uhy4EEL0bYGzZmJNTaHw5lvIv+JKYh95GL+JE/WO1atER19Mefk7VFT8j4iIaScdNyN5Bn//9O8crj5MRnBGNyYUonudbprHl+5SVfV+IAZYC3yhaVqW52L1bmazmX79+tGvX8d8s7a2NoqLiykqKqKwsJAjR46wZ88eAKxW6zfKdVxcnFzMKIQQp2Dr35+k5cspvOlGCm+6mci7/0jIFVfoHavXCA0Zj9UaRUnpilOW6WnJ0/jnjn/yTs47ZIyQMi16r66W6eeAdcC5nY+fA+RX/TPEYrGQnJxMcnIy0HEldFVVFYWFhRQWFlJUVMSmTZuAjgs7oqOjSUxMJDExkYSEBJkaIoQQ32KOjCBpyRKKf3sHZX+5n/b8AiJ+dweKXKfyoymKkeioueTlP01raxlWa+QJx4XYQjgr+izW56/nl8N/iaIoJxwnRE/X1TIdqmna86qqLtA07WNVVeVfhAcpikJoaCihoaEMHToUgJaWFoqKiigoKCA/P59PP/2UTz75BICIiIjjZTwpKQmbzaZnfCGE8AoGX1/i/vM4Zf94kKoXX6StqIjYh/6JQU5A/GjR0ReTl/8kpaWrSEq68aTjpiZO5d5P7uVQ1SH6hZ549Q8herqulmlUVc3svI8DZKu/bmaz2Y7PuQZob2+npKSE/Px88vLy+Oyzz9i+fTuKohATE3O8XCckJMhSfEKIPksxGon64x+wxMdT9o9/kH/VT4l/6klM4eF6R+vR7PZkggJHUVK6gsTEG0561vn8hPO5f9v9rM9fL2Va9FpdLdO3AYuBfsBK+vCa00UH9hGVrmLSuaCazebjUz0mTJiAw+GgqKiI3NxccnNz+fjjj9myZQsmk4nExETS0tJITU0lPDxcvmoTQvQ5IT+9CnNcHMW/+Q15Vy4g4fnnsPSQ1aC8VXTMJRw8eCe1tZ8RFDTyhGOCbcGMihrF+rz13DbsNvn5I3qlUy6N93WqqoYCqUCOpmkVHk11+ixJ6LA0nsvl5NEr5jJi5oVMXODd62a2trZSUFBAdnY2WVlZVFR0/CcLCAggNTWV9PR0UlNT5WJGIUSf0rRrF4U33oTBYiH+2WexqXJh3A/lcDSyZesYIiJm0L/fP046bsXhFfzlk7+wYtYKMkNkqULR85xuabwurbmmquo84GPgD8A2VVUXnMmQPYXBYCRz3ER2r19LU12t3nFOyWq1kp6ezrRp0/jFL37B7bffzqxZs4iNjeXAgQO89tpr/POf/2TJkiVs376d6upqvSMLIYTH2YcNI+nlJaAo5F91FU27dukdqccymXyJiJhBeflaHI7Gk46blDAJo2Jkfd76bkwnRPfp6gLGvwJGaJp2ITAM+KXnInm3s+bOw9HWxmdrVukd5XsJCgpixIgRXHbZZfzud79j4cKFnHXWWdTU1LBu3Tr+/e9/88QTT/D+++9TXFxMV7+xEEKInsaank7iq69iDA6i4NrraNi8We9IPVZM9CU4nU2UH1t30jEhthBGRo1kff56+dkieqWulmmXpmkNAJqm1QMtnovk3UJj41HHjmfXe2tprq/TO84PYjQaSUpKYurUqdx6663ceuutXHDBBfj5+bF161aeeeYZHnnkEdatW0deXh4ul0vvyEIIcUZZ4mJJeuUVLElJFN50M7Vr1+odqUcKDByB3Z5MacnKU46bmjiV/Lp8Dlcf7qZkQnSfrl6AmK2q6v8BHwHjgWzPRfJ+Yy66DO2TzXy29i3Gzb9K7zg/WmhoKGPHjmXs2LE0NTVx+PBhDh48eHyFELvdTmZmJgMHDiQpKUl2ZBRC9AqmsDASX3qRoptupuS3d+Cqryd4/ny9Y/UoiqIQHXUJ2TkP0dSUi92efMJxkxIm8dftf2V9/nrUELWbUwrhWV0t0/+lY5OWKcDlwAUeS9QDhMUnknHWOex6dzUjZ87F5uend6Qzxm63M3ToUIYOHUpraytZWVkcPHiQffv28fnnn+Pr60v//v0ZOHAg8fHxUqyFED2a0d+f+Gefofj2X3H03vtwNbcQes1CvWP1KNHRc8nO+T9Kj75JasqvTjgm1CeUUZEdq3r8YugvZFUP0at0tQk9DKzSNO0XwKjO533amIvn09bczGfvvKV3FI+xWq0MGDCASy65hDvuuIN58+aRmJjIrl27WLx4MY8++ijvvfceR48e1TuqEEL8YAabjbjH/o3/tGmUP/ggxxYtkrm934PVGklI8FjKjq4+5d/b1KSp5NXlcaTmSDemE8LzulqmHZqmHQDQNC0H6POTaMMTkkgffTa71q2mpbFB7zgeZzab6d+/P/PmzeOOO+7goosuIioqiu3bt/PUU0/x5JNP8vHHH1NfX693VCGE+N4Ui4XYfz1E4Jw5VDz2OMceflgK9fcQGTWb5pYC6up2n3TMpIRJGBSDrOohep2uTvPIV1X1b8AnwGig2HOReo4xF8/nyKcfs2vd24y95HK943Qbq9XK4MGDGTx4ME1NTezbt489e/awfv16NmzYQGpqKkOGDCEzM1N2XxRC9BiKyUT03/+G4mOj8plncTW3EPmHu1BkOttpRYRfgKb9iaNH3yIwcNgJx4T6hDIysmNVj1uG3iJTPUSv0dVPiGuAcuAnwDHAu3cs6SYRSSmkjhzDZ++8SWtTk95xdGG32xk9ejTXX389t9xyC+PGjaO8vJzXX3+dhx9+mHXr1lFeXq53TCGE6BLFYCDqz38mZOFCql9+mdI//Qm306l3LK9nMvkTFjaJsvK1uFztJx03NXEqubW5ZNVkdWM6ITyrS2emNU1rAR71cJYeaezF83n5rm3s7R/23wAAIABJREFUfm8NZ82dp3ccXYWHhzNp0iTOO+88cnNz+fzzz9mxYwfbt28nLi6OESNGMGDAACwWi95RhRDipBRFIeLO32Gw26lYtAh3Wxsxf/87itGodzSvFhU5m/Lyd6iq2kJY2HknHDMp8atVPdKD07s5oRCe0dVpHqLT9poGSlvbMSoKRgVMAeE0nTeD5Z/tomns+dhsNoyASVEwGhRMioIBMBy/BwNKx72iYFY6xpgVMBm+fKxg6MFffxkMBlJTU0lNTaWxsZE9e/bw2Wef8dZbb7Fu3TqGDh3KqFGjCA8P1zuqEEKckKIohN92K4rFwrFHH0Uxmoj+6wMy5eMUQkMnYjIFcbRs9UnLdJhPGCMiR7AhbwO3DL2lmxMK4RlSpr8Hp9vN/D3ZNLu+dVGKOhbUsbx6sOiM/VlGha8VbQWTQcGiKJgNHc/NX39sULAohs77r163dN5bDV+9ZzEoWAwGrF97bjUYOl5Xvnps7Rxj7Rxv+9prFkXp8lw3X19fzj77bMaOHUtBQQE7d+5k586dfPrpp6SkpDB69GgyMjJkiT0hhFcKu/EG3A4HFf/5D4rJSNR990mhPgmDwUJkxHRKj76Jw9GIyeR7wnFTk6byt+1/I7smm9Sg1G5OKcSZJ2X6ezAqCjvHDqCy3YHT7cbpduNwg8vtZsOLz1BdfpTpv7wTt9F4/PV2txuXG1y4cbs7lkFxud24AIfbjcPl7rh3u2l3dxT2NteXzzveb+t8/8vX21xu2t0u2l3Q7nbR5nLT6HLS5nDT7up4v83tps3lov34eDet3/4l4Ef4erm2dd77GAxYDQZsxo7XbJ2PfQwGfAwGbEYLthHnEDhkNMeKivggN4cN739E4JbtDMzIYEhmBsG+dnwMBuxGA3aDAR+joUefpRdC9Hxht9yM2+mg8smnwGgk6s9/lovnTiIyag7FJUupqHifqKg5JxwzJXEKf9/+d9bnreemoTd1c0Ihzjwp099TqMVEqOW7f22h557Lyr/eTcjeHQw6f6oOyU7P3Vn+21wuWjtLdqvLdbx8H3/sctPS+bi1c2yL88vnHe+1fvle5/OOW8drLU43Ne3ttLhcNLtcNDu/GuM83ud9IGnA8WwrncD+whPm9jEo+BgN+BqN2I0GfDuLtq+p4zVfY0f59jN+9dzPaMDP9OVjI34mA/6d93aDQX4QCiG6rGPKx23gcFD5zLMoRhORd/9RPkdOIChwBDZrDEfL3jppmQ7zCWNw+GC2lGyRMi16BSnTZ0jCoCFEJKWy8+03GHjuZK/8GlDpnJttNhg58ZdvntfWWbqbnR3lusnZUbiLj1Ww68BBsgoLaTcYCY2JJTopGbO/P81OF43Or8Y2dT6vaWmn0dlCo9NFQ+f7XWGAr5VrI/5GA/4mIwGdN3+jkUCTEX+TgcDO1wJNRgLMxuPPpZAL0bcoikL4r3+Nu91B1QsvoJhMRPz+Tvkc+BZFMRAZNZuCgmdoa6vAYgk74bjhEcN5+eDLtDpbsRqt3ZxSiDNLyvQZoigKo2ZfxNrHHiL78x2kjTxL70heyWIwYDFAgOmbV8UPD/BlVmoidXV1bN++nZ07d9L6+SdEJyRwzjnnkJGRcdofWi53R0lvcLpocDo77h1f3dd/7Xm9w0m900mDw0Wdw0lVu4P85jbqOl8/3ZQYi6IQYjYRbDYSbDYRYjYSYjYRajYRYTUTYTERYem4D7eYsRu975crIcT38+UqH26nk6oXX0SxWIj4za/1juV1oiJnk5//FGXl7xAf99MTjhkSMYTF+xdzsPIgQyOGdnNCIc4sKdNnUMaYcWxe+hI7Vr8uZfoHCggIYMqUKUyYMIHPP/+cbdu2sXTpUqKiopgwYQKZmZknvVjRoCj4moz4moxE8uM2i2l1dZTsOoeT2m/d17Q7qXE4qW53UNXuoLrdidbYQlV7x2snOj/ubzQQZTUTaTET2XkfZTURaTUTY7UQ3fma2SBnuYTwZoqiEPmHu3C3t1H5zDMYg4IIvU62Xvg6Pz8VP79Mjh5dffIyHT4EgD3H9kiZFj2elOkzyGA0MnLmhfxv8dMUHzpAbGZ/vSP1WFarlbFjxzJ69Gi++OILNm/ezGuvvUZ4eDjjx49nwIABGD245qvVYCDcYiDc8v1KudPtpqrdQVlrO+VtDsrbvro/2tpOWauDT2sbKW9r/87ZbwWIsJiI6izYsbav7mM77yMsZozytbIQulIUhah77sFZW0v5Qw9hDAkhaO6FesfyKlGRs8nK/idNTfnY7YnfeT/MJ4w4vzh2l+/m6gFX65BQiDNHyvQZNvDcKXy8cik73n5DyvQZYDQaGTZsGEOGDGH//v189NFHvPHGG2zatInx48czePBgj5bq78uoKIRbzKct4W63mxqHk9LWdkpbO4p2SWvb8ec5za1srq6n4VvzwE0KxFgtxNu+dvPpuE+wdZzhltVPhPA8xWgk5sEHKaqtpfTuuzEGBuJ//onXVu6LIiNnkZX9EEfLVpOSfOsJxwyNGMq20m243W6Zey56NCnTZ5jZZmPo1Blse30plcWFhMbG6x2pVzAYDAwaNIgBAwagaRoffvghb731Flu2bOH888+nX79+PWqtakVRCDabCDab6O/nc9JxdQ4nxS1tFLW0UdLaTlHn48KWNj6oqqOszfGN8RZFIcGno1gn+lhJtFlItltJ9rGSYLNgk7nbQpwxBouF2Mcep2DhQop/9SsSnn8O+4gResfyCjZbDEFBoykre4vkpF+csCwPDR/Kmpw1lDSWEOsXq0NKIc4MKdMeMGzaTHaufp3P1qxi6g236R2nVzEYDPTr14/MzEwOHjzIBx98wIoVK4iKiuL8888nPT29V53hCDAZCfDzod9JCneL00VJazsFLa0UNLeR39JGfnPH4511jdQ5vjqzrQCxNjPJPh3lOsXHSpqvjTS7lXibRaaPCPEDGP18if/v0+RfuYDCG28i8eUl2FRV71heISpyNoe0P1Jfv5eAgMHfeX9IRMe86d3lu6VMix5NyrQH2AMCGXDeFPb97z3OnrcAv+AQvSP1Ooqi0L9/fzIzM9m7dy+bNm3i1VdfJT4+nkmTJpGUlKR3xG5hMxpIsVtJsX93aSm32021w0lecyu5Ta3kNreR29xKTlMrq8trqHE4j4+1KArJditpditpdhsZdisZvjbS7DZ85Gy2EKdkCgkh4dlnyLviSgp+9jOSli7FEhendyzdRURMRzt8H0fL3j5hmU4LSsNusrO7fDczUmbokFCIM0PKtIeMnHEhX2xYx651qxl/xUK94/RaBoOBIUOGMGDAAHbt2sVHH33ECy+8gKqqTJkyhbCwE69x2hconcv3hZhNDA/47srilW0OsptayGpuJauxlezmFrTGFt6rqMXReW2kAiT6WMiw28jwtdHP10Y/Px/S7FYsPWhajRCeZo6N7SjUC66i4LrrSFq2DFNwsN6xdGU2BxIaMo7y8nWkp92FonzzM8NkMDEofBB7ju3RKaEQZ4aUaQ8Jioomfcw57NmwjtEXzsNqt+sdqVczmUyMGjWKoUOHsm3bNjZv3syiRYsYOXIkEydOxNdXr21qvFfHbp5+jA7y+8brbS4Xuc1tHG5s6bg1ddx/UFVPu7ujZZsUSLXb6N9Zrgf4+TDIz4cI649bklCInsyank78k4soWHgNRbfeSsLzz2OwWPSOpauIiOlUVP6Puro9BAYO+877Q8KH8Nze52hqb8Julp+TomeSMu1Bo2ZdxOFPNrN347uMnHWR3nH6BLPZzPjx4xk2bBibNm1ix44d7NmzhwkTJjB69GjMZil7p2MxGFB9bai+tm+83u5yk93cwsGGFg42NHOwsYUddY2sKq85PibcYmKgnw8DOwv20AA7iTZLr5rHLsSp2IcPJ/pvf6Pkt7/l6D33EP2Pf/Tp//+HhU1GUcyUl687YZkeGj4Up9vJvop9jI4erUNCIX48KdMeFJWaTvyAwXz+7tsM/8kcDF60hFtv5+fnx8yZMxk9ejQbNmxgw4YN7Nixg2nTpqGqap/+4fZDmQ0Kmb4+ZPr6MDfyq6+va9sd7G9oYX9DM/samtnX0MSThfXHp4oEmowM8fdhsL+dIf52hvj7EC8FW/RigTNn0FaQT8Vjj2NOTCT85pv1jqQbszmAkM6pHmlpd33n3/3g8I651HuO7ZEyLXosKdMeNnz6bN761wNk7dxGxlnn6B2nz4mIiODKK68kOzubd999l2XLlpGWlsb06dMJDQ3VO16vEGg2cXawH2cHfzVdpNXl4nBjC1/UN7Onvond9U08XXjs+DSRMLOJ4QF2RgT4MjzAztAAO/4m+WVT9B5hN91Ee35HobYkJBI4s+9eYBcZMZ0DlR90TvX45m6HgdZAUgJT2H1st07phPjxpEx7WMqIUQRGRLJr3dtSpnWUmprKjTfeyPbt29m0aROLFi3inHPOYdy4cVj6+JxGT7AaDAzytzPI386VdPzS0upycbChhd31Teyqa+LzukbWV9YBHRc6ZvjaGBXgy+ggX0YH+sr0ENGjKYpC1P33015cQukf/oA5Jgb78O9Oc+gLwsKmdEz1OLbuO2UaOjZv2ViwUTZvET2WlGkPMxiMDL1gJh8ueY7yvBwiklL0jtRnGY1Gzj77bAYOHMiGDRv46KOP2LNnD9OmTSMzM1M+xD3MajAwtPMs9MLOJWVr2h3srm/is9omdtY1svpYNS+XVgIdW6uPDuwo1mOC/Bjg5yNrYYsexWCxEPv4Y+TNn0/RLbeQ9NpyLPF9byOvjqke53RM9Uj9/Xc+a4eGD+WNI2+QV5dHcmCyTimF+OFkbatuMPC8KZitNj5/Z7XeUQQQEBDAxRdfzMKFC7FarSxfvpxly5ZRV1end7Q+J8hs4tyQAH6THMXSIakcGjeID0apPJgRx/hgf/bUN/OnrBKm7jxMvy17+ekXOTxVUM4X9U04O6eMCOHNTMHBxD/1FLhcFN5wI86GBr0j6SIiYjotLcXU1+/9zntDwr/avEWInkjKdDew+frRf+IkDm3dRFNtzekPEN0iKSmJG264gcmTJ5Odnc0TTzzBzp07cblcpz9YeIRBUejn58PVsWE80T+RHWP78/nY/jzZP5E5EcFkN7Vyb/ZX5frqvTk8W3SMw40tuKVcCy9lTU4m9vHHaCsooOTO3+Pug58x4Z1TPcrK3/nOe0mBSQRYAmS9adFjSZnuJsOmzcTpcPDF++/qHUV8jdFoZNy4cdx0003ExMSwZs0aXnzxRSoqKvSOJjrF2CzMjQzmITWerWP6sevs/izqn8js8GC0xhbuPlLMhE8PMeKTA/zyYAGvH63iWFu73rGF+Abf0aOJvPNOGjZupOKpp/SO0+3M5kBCQs6mvHzdd37xNSgGhoQPkTIteiwp090kNDaepCHD2b3hHZwOh95xxLeEhoby05/+lNmzZ1NWVsaTTz7J5s2bcTqdpz9YdKtoq4WLIoP5V2Y828b0Z/uYfjykxjEiwJf1FbXccrCAQVv3M3WnxoM5peysbZQpIcIrBC+4ksA5s6l4/D/Uf/CB3nG6XUT4dFpaik461SOrJou6NpluJ3oeKdPdaNj0WTRWV3F4+1a9o4gTUBSF4cOHc8stt6CqKhs3buS5557j2LFjekcTp5DoY+WqmDCeGZjEvnEDeW9kBr9PjsJmMPDv/DJmfn6EgVv2cdP+PFYcraKkpU3vyKKPUhSFqPvuw9ovk5I7fkdrbq7ekbpVePgUFMVEefm677w3NKJjlY8vjn3R3bGE+NGkTHej5CEjCI6OYZdciOjV/P39mTdvHpdeeinV1dU8/fTTbNu2TeZS9wBGRWGIv53bk6JYPTyd/eMG8lT/RKaEBbC5uoFbDxYw/JMDjN12gF8fKmCllGvRzQw2G/GPP45iMlF06604Gxr1jtRtzOYggoPHUnaCqR6DwgZhUAwy1UP0SFKmu5FiMDD0glmUZmmUHtH0jiNOY8CAAdx8882kpKTw7rvvsmTJEmpq5ALSniTYbOLCyGAe65fIF+cMYP3IDO5LiyHD18baY7X8orNcj9l2gNsO5vNySSVaYwsumRYiPMgcG0vso4/QlpNL6V139amLZyMjfkJLSyH19fu+8brdbCcjOENW9BA9kpTpbjbw3ElYfHz4fJ2cne4J/P39ufzyy5k9ezbFxcU8+eST7Nmzp0/98OstDIrCYH87N8RH8OKgFA6MG8iGznKd6Wvj/co6fqsVMvHTQwzYso+rvsjh8fwydtQ20ibfSogzzHfMGCJ++1vqN2yg8r/P6B2n23RM9TCecKrHkPAhfHHsC5wuuVZF9CyyaUs3s/jYGXjuFHavX8vEBdfiFyJbWnu7L+dSJyUl8eabb7Jq1Sp27tzJ2WefjaqqGAzyO2lPZFSU47s03hAfgdvtJru5lU9rG9nRedvQuUOjj0FhVKAvY4P8ODvIj6EBdqzy3138SCHXLKRl3z6OPfooLQcPEnrdtfgMGqR3LI8ym4MJDu5Y1SM19Y5vbOAyJHwIy7XlZNVkoYaoOqYU4vvx2jKtqqoBWAQMAVqBn2malqVvqjNj6LSZfP7u22xb9Rpj5s7DNzhEdt/rAUJCQli4cCGfffYZW7duZfny5YSEhDB27FiGDBki25L3cIqikGa3kWa3cUV0xy+5FW0Ottc28HF1A5/UNPBg7lEAbJ3lekKwP+OD/RnkL7sziu9PURSi//oA5thYqpcto/7dd7GPHk3oz67Dd/z4XvtzISJiOocO/YH6hv0E+A88/vqXFyHuObZHyrToURRv/bpaVdWLgNmapi1UVXUMcJemaXM630sCcjdu3EhcXJyeMb+jzeGiqc1BQ6uDpjYnDa0OHM6Ov+Ov/10fevU/VOzdAYDJ7odvVBz2qHh8o+KxhUSgGHrnh2hv4Xa7qKwop6Qon4aGOkwmM1Ex8QQGBkMv/QHYW7mdbtob2nG7Tv9Z2GgwkGuzke3jQ5bNh1KrFQAfp5O0lmbSm5qJbPeuCxoNjhaM7U16x+iRFMDkNIG7G/5Nu9xQUwtVteB0gMUCIUFgMXv+z+5uxlZ8BqzB1RiKqzEUt8uM22kBh5ljLQ2YsOBr8NE7pfBCkTZ/rll4a7f/uUVFRUyaNAkgWdO0vG+/77VnpoFxwLsAmqZtU1V1pM55cLnc/OPdQ+Qca6Cx1UlTW0dhbmpz0tjmoKnVSZuza3MrDe5hREXFENZWSWh7JWHFlYTmZmF2yxrUPY2Pjx/toZEUOdop0juM8DgbMKDz1mS2UhwcTnFQOLnB4ewND9c5nRA9xVngT8dNiC4yuh3MqawgJDRM7yjf4M1lOgCo/dpzp6qqJk3TdG2bB0rqqGpsw9dqJNBuISbIiN1iwm4x4ms14fvlvfXL5yYspm/OrTzZOQ63y0VrdQWtNbL7Xk/U0tJEa2uL3jHESThbnNQXNNBa2YqjteMCJ5PNiDXEhjXYgsH0w+ZADwCob8VdX0Sl2UyNSd+PVQU3loYifOpyUdwOWu0xtNsjT/7BIzC3mwlpCMLQeU2+S3HSZnLgMLbTbnTgUnS4ANUNtLVBX7j4VXGiGNtRjO24jG04FO/6dkd4j2izLyHn635u9Tu8uUzX8c3fWQ16F2mDQeHln53l4T8lwsP/+0L0LW63m8OflvHRUg3FGUpavxAS+oeQMCCEwHC73vHOHLcbDq2FDX+CqhxIOQ+mPgBRA09/bB/WfKCSylcPYgrxIXB6EpZYPwz+ll47X1kIceZ5c5neCswCXuucM/3d/UeFEOIUWhrb+fBVjazPyolODWTSwv4EhvfCuZhtjbB8AWT/D8JUuHIlpE2W+fun0bS7nKrXDmOO8SXsmoEYfXvh/GQhhMd5c5leBUxRVfVjOr6gvEbnPEKIHqTwYBUbXzxIc10bZ81JYfgFiRh644W9TgesuAZyNsH0f8LI68DozR/t3qFheyk1b2ZhSQok7Or+GGzydyaE+GG89tND0zQXcKPeOYQQPYuj3cm2VTns+V8hwVF2fnLTCCISA/SO5RluN6y5HY68BzMfgZHX6p2oR6j/sJDadXnYMkMIvTITxWzUO5IQogfz2jIthBDfV2lWDf9bcoiasiYGnRvH2ItSMVt6cVHa9HfYtQQm/E6KdBe43W7q1udT/0EhPkPCCZmXgWKUzXeEED+OlGkhRI/X1uJg21s57N1UhH+wjdm3DSW+f4jesTxr5/Pw4YMwbAGc9we903g9t9NF9RtZNH1Whu/oKIIuTJP1/IUQZ4SUaSFEj1Z4oIoPXjlEfVULg86NY8ycFCy9ff7robWw9jeQPhVmPioXGp6Gq8VB5SsHaT1Sg/+kBAImJ8hqHUKIM6aX/8QRQvRWrU3tbF2ZxcGPSwmKtHPRb4YTnRakdyzPK/wUVl4L0UPh0hfAKCtQnIqztpWKF/bTXtZE8MXp+I6K0juSEKKXkTIthOhRvlw3euvKI7Q0Ohh+QSKjZiZh6gsXkZUdgFfnQUAMXLkCLL56J/Jq7UcbqVi8D1ezk7CFA7BlBOsdSQjRC0mZFkL0GFUljXy4VKPkSA2RyQHMulUlPKGP7EdcmQ0vzQGjFRa8Ab7etZ2ut2nJqqZyyUEUq5HwGwdjifHTO5IQopeSMi2E8HptLQ52vpPHnvcLMduMnHulSv9zYvrOBWTV+fDibHC7YOEaCEnWO5FXa9xxlOpVWZjCfQi7ZiCmIKvekYQQvZiUaSGE13K73eTsOsaWFUdoqG6l39nRjJ2bio+/Re9o3aeuBF6aDW31sHAthKt6J/JabqeL2rW5NHxcgjU9iNAr+8lmLEIIj5NPGSGEVyrPr2PryixKjtQQGuvH1J8NJDo1UO9Y3avhWMfUjsYK+OlbEDVI70Rey9nYTtWrB2nNrsVvXCyB05NRjH3kmwshhK6kTAshvEpjTSvb3szm0Paj+PiZmXiFSv9zojH0tc01mqpgyVyoKYQFr0PcSL0Tea32o41UvHQAZ20rwZdm4DsiUu9IQog+RMq0EMIrtLc52b2hgM/fy8flcjNscgIjfpKE1acPfky11MErl0CFBlcsh6Rz9E7ktZr3V1K1XEOxGgi/YTDWhF66dbwQwmv1wZ9SQghv4nK6OPTJUXaszaWhupXUYeGMvSiVwHC73tH00VwNL18MpXtg3hJIPV/vRF7J7XJTt7GA+o0FmOP8CLuqP8ZAudBQCNH9pEwLIXThdrnJ3nWM7atzqClrIjI5gMnX9Ce2L68F3FTVMUf62KGOIp35E70TeSVnQxtVyzRas2qwD48geG4aSl9YZ1wI4ZWkTAshupXb7abwYBXb3szhWEE9wdG+TL9xEMlDwvr2Fs9fXmxYmQXzl0L6ZL0TeaXWvFoqXz2Eq8khOxoKIbyClGkhRLcpOVLNp2tyKdZq8A+xMWlhPzJGR2HoK+tFn0z90Y51pGsKOuZIp56ndyKv43a7afiomNr3cjEF2wi7eYhsxCKE8ApSpoUQHuV2uyk+XMOONbmUHKnBJ8DCuHnpDBwfi9Hcx1boOJHaYnhxVkehXrASksbpncjruJraqVpxmJaDVfgMCiP44nRZP1oI4TXk00gI4RFut5uiQ9XsWJtLaVYtvoEdJXrAuBhMFpnfCnTsbPjSbGishKvegIQxeifyOq05tVS9puGsbyNwVgp+Z8f07elAQgivI2VaCHFGuV1u8vZW8Pl7+RzNqcMv2MqE+Rn0Oycak1wk9pWy/R2rdrQ3dWzIEjdC70Rexe10Ufd+AfWbCv+/vTsPj+O+7zv+3vsCFov7JEgQAIf3IeqiJOqWD8WObCm2ZFk+5LixnfRJkzRNmh5pnKZP4jZukraO6zbO4UNxLV+yLVuSJVu3KVESSZEiMSQAEvd9LhbYe/rHgCJ12SQEYLDA5/U8+8zsLBb8EsBgP/jtb74/vGVBqj69C/+6YqfLEhF5A4VpEVkUuUwe8/lBDv+km4nBWYrLglx3t8GWfbWazvF6Xc/CfXeBPwz3PgTVW52uaEXJjM4x/o02Mr0zhC+tJvbeZtwB/SEmIiuTwrSIvC2puSyvPNnHkZ/2MDuVpmJdEbf8+lZaLqlae6sWXoi2B+Fbn4CSdfbUjlij0xWtGJZlMfvCEJM/6MDldVN+zxZC2yucLktE5BdSmBaRBZkcnuXY430cf7afTDJHw+ZSbv7YVhq2lGpO61t58Z/gh78DdXvg7vshUu50RStGLp5m4rvtJI+PEWiJUfaBTVqERUQKgsK0iFywsz2iX/5ZL13HxnC7XDTvrWLPLY1UNmo+61uyLHjq8/DT/wzNN8GdXwV/xOmqVgTLspg7PMLkDzrIp3OU3NpE0TX1uNZ6u0QRKRgK0yLyS6WTWcwDgxx9vJeJwVlCxT4uu3UD266tJ6LRw18sl4WH/hAO/h3s+CDc9gXw+p2uakXITaeZ+O4pkifG8TcWU/prm/BVrdFl5EWkYClMi8hbGumOc+ypPk49P0QmlaNqfTE332vPh9ZFhRcgOQX33wsdj8FVvw03fxbc+rpZlsXsS8NM/qATK5un5FeaKLpao9EiUpgUpkXkNdLJLKcODvHKU/2MdMfx+ty0XFrFtv31VDdFNR/6Qk2cgfvutJcHf+//gL0fc7qiFSE7nmTygXaS5gT+9VFKf60VX6VGo0WkcClMiwiWZTHYMUXbgUFOHbRHocvqIuy/cxPGFdUEwj6nSywsPc/DP38I8hm45zuw8TqnK3KclcsTf6qP+GPd4IKS98wvwKLRaBEpcArTImtYfDyJeWCAtp8PMjUyhzfgoWVPJduu1Sj0gh39FnzvN6GkHu7+JlS0Ol2R41Jnppj4bjvZoVmCW8uJ/Woz3pjm2ovI6qAwLbLGpOeydB4eoe3AIH0nJ8CC+k0xLr11Axv3VOIP6tfCguTz8MTn4Im/gPVXw51fg3CZ01U5KpfIMPXj08y+MIQnFqD8o1sJbVU7QBFZXfSqKbIsZJefAAAgAElEQVQGZNM5uo6NcergEGeOjpHL5olWBLn8PU0YV9QQrQg5XWJhS83Adz8FbT+E3ffAe/5qTXfssHIWiYODTD9yhnwyR9F1DURvasTt1yqGIrL6KEyLrFK5bJ5ec4JTB4foPDxCJpkjFPWzdX8dmy6r1jSOxTJ+Gr5xN4y0wTv/HK78DKzhr2uyfZKpH3aQGZzF31RC6W3N+GrUU1tEVi+FaZFVJJvO0X18nM5DI5w5OkpqNos/5KXlkipaL6umflNMS3wvps4n4P6P2Yuy3PMdaL7B6Yockx2bY/JHp0m+MoanNEDZh7cQ2l6uP9hEZNVTmBYpcOm5LN3Hx+k4NEzX0TEyqRyBsJemnRVsvKSKxi1l6gm92CwLnv+/8NC/tS8wvOs+KG92uipH5JNZ4o/3EH+qD5fHRfSd6ym+pgGXfuZEZI1QmBYpQNNjc5x5eYwzR0fpMyfI5yxCxT5aL6+meU8l9UYpHo1AL43MHPzo38Chr4JxK7z/SxCMOl3VsrOyeWYODBD/aTf52SzhS6ooedcGPFF16RCRtUVhWqQA5HN5hs7E6To2ypmXxxjrmwEgVh1m543raNpZTk1zDLd69i6tsQ57WsfgUbj2D+D6P1pzKxpaeYvZw8NMP9JFbjJFoDVGyTs34G8odro0ERFHKEyLrFCJyRTdx8foOjZOb9s4qdksLhfUtsS46o4WmnZWEKvWynHL5vgD8L3fAo8X7r4fNr3D6YqWlWVZJM0Jph86Q2Ywga++iNI7Wgm2ljpdmoiIoxSmRVaITCpHf/skvW0T9Bwff3X0OVzip2l3Jeu3ldOwuZRgRKsRLqtsGn7yx/DcF6H+UvjAP0JsndNVLRvLski1TzL9aDfprmk85UHKPrSZ0I4KrV4oIoLCtIhjcrk8w2fi9LaN09s2wWDnFPmchdvronZjCfve30zjtjLK64vUEcEpkz1w/8eh7wW44jNwy5+umf7RbwjRJX5i72smcmkNLu/amtoiIvKLKEyLLJNcJs/QmWn6T03Sf2qCgc5psqkcuKByXTG7blpHw+ZSalti+LS4hfOOPwDf/23I5+AD/wTb3ud0RctCIVpE5OIoTIsskdRclqHOKQY6pxg4Ncng6WlymTwA5fURtuyrpX5TjPpNpQSLNHVjxUjNwEN/CIe+BnV74I4vr4m2d1beInlinPgTPaS74wrRIiIXSGFaZJEkplL0tk0w0DHFYMckY/0JsOzF8Mobiti+v566TTHqWmIKzytV7wvw7U/CxBnY//tw/b8Fz+r+XlnZPLOHR4g/2UN2eA5PWVAhWkTkIihMXwQrl2fsvjYil9cQMsqcLkdWiInBBC893MXJ54bI5y18QQ81G0vYuKeK2uYSqpui+IM61Va0XBae/u/w+F9AtA7u/RGsv8rpqpZUPpUj8fwgM0/3kptK46uJUHaXQWhHJS6P5uiLiFwovcJfDLeLfDzN2FdPUPmJbQQ2xpyuSBw0dGaalx7uovPwCF6vm23X1bPlqlrK64vU77mQjLbDA78FPQdgxwfg1r+E0Oo9t7MTSWZ+3k/i+UGsZA5/Uwmlt7cS2FSqC11FRBZAYfoiuFwuyj+2jZEvHWH0n45T+Rs78dcXOV2WLLPetnFefKiL3rYJAmEvl757AztvaCBUvDa6PKwauQw8+z/t0WhvEG7/v7Dzg05XtSQsyyLdNc3M033MvTIGLghtr6DomnoCjWtv9UYRkcWkMH2RPBEfFb++g5EvHmH0749S+eld+Cq1cMZaMDUyxzPfOsXpI6OES/xcdXsL2/bX4Q/pNCo4A0fggX8Jgy/Dlvfao9HFNU5Xtegsy2Lu6CjxJ3rJ9M3gCnkpvq6ByJV1eGNa9ltEZDEoBSyAtyRAxa9vZ+RLLzP6d8eo/MwuvTCtYpl0jpce6uLQI924PC6ufN9Gdt20Dq9P7esKTmYOnvgcPPM/IFIBH/wKbL3N6aqWRHY8ycT32kmdnMBbGSL2/hbCe6pwq+2iiMiiUpheIF9lmIpPzAfqLx+l8lM78RTpbf7VxLIsOl4a4Zlvn2JmPEXrZdVcdXszRaVBp0uThWh/DH78BzDWDnvugXf8GYRW31LYVs5i5pk+pn/SBS4XsfduJLKvTqsViogsEYXpt8FfV0TFx7cx8uVjjP7DK1T+ix241bVhVRjtjfPMt9rpbZugvD7Czb+3lfpNqy94rQljHfDwv4eTP4bSJvjI96D5BqerWhLp3jgT3z5FZiBBcEsZsdta9K6ZiMgSU/J7mwJNJZTfs4Wxrxxn7GsnqLh3Gy6PerMWqpmJJM890Enbc4MEQl7237mJ7dfW4db3tPAkp+HJ/wYHvmhfYHjLn8IVnwbv6guXVi7P1MNnmHmqD3eRn7IPbyG0vVzdOUREloHC9CIIbS6j9I5WJu4/ycR32ym9o1UvYgUmNZflpYe7OPJYD5ZlsfvmRva+az3ByOpesGNVyufg8NfhsT+FxCjs+TDc+MdQXO10ZUsiP5th7OsnSHVMEbm8hpJ3N+HWRbEiIstGv3EXSWRvNdnxJPHHuvGWBYne2Oh0SXIBctk8rzzVz8EHT5OcydB6WTVX3raRaEXI6dLkYlkWtD8Kj/4JDB2DdVfA3d+E+kucrmzJZIZnGfunV8hOpij9wCYie1fnHwwiIiuZwvQiit7cSG48yfQjXXjLgoR3VzldkryFfC5P24FBXvjRGeJjSeo3xbjqjhaq1qvnbkHqfQF+8p+g62l7XvSv/T1su91ey32VSp6cYOy+E7i8bip/YycB/eyKiDhCYXoRuVwuSu9oJTuZYvz+k3iiAQIbS5wuS86Tz1ucOjjEwQdPMzU8R9X6Yq77kEHjtjJNzSlEo6fs6Rwnvg+RSrtf9CUfA+/q7axjWRYzz/Qz9WAnvpoI5R/dilcdZkREHKMwvchcXjcVH9nC8BePMPrV41T9phZ1WQmsvEXHoRGe/+FpJgYSlNcX8e5P76BpV4VCdCGa6IKn/hIOfR18Ibj+j2Dfb0Gg2OnKlpSVzTP5/Q4Szw8S3FpO2Z0G7oD6RouIOElhegm4wz4qPr6N4b89wug/vELVb+5SD2qH5HN5Tr0wzEsPdzHen6C0Jsw7PrmNlkuq1He3EE10wVOfty8wdLnhsk/Ctb8PRat/SlV2MsX410+Q7olTfMM6ores18+wiMgKoDC9RLzlIco/tpWR/3OUsa+eoPJf7MDlVXu15ZLL5Gk7MMBLj3QzPTJHWV2Em+/dSutl1bgVQArPZLcdog99zQ7Re++Fa34XSuqdrmxZJE9NMP6NNqysRfk9Wwhtr3C6JBERmacwvYQCjVHKPriJ8fvamHygg9jtLZpSsMQyqRzHn+7n0E+6SUymqFpfzNWf3kHTzgqN4hWisQ545m/g8H32xYR7Pz4fohucrmxZWHmL+OM9TP+kC29VmPJ7tmjamIjICqMwvcTCOyvJDCSI/6wHX12Eon11Tpe0KiUmUxx9vJdjT/WRSmSpa41x00e30LClVH/AFKL+w/DMX8PxB8Dtg0s+Avv/9ZoJ0WD3jx7/5kmSbeOEdldSensrbr/mR4uIrDQK08sgest6MgMJJn/Qia86TGBjzOmSVo3R3jiHH+3h1MEh8nmLjbsr2X1zI7XN6qJScCwLTj9ph+iOn0IgClf/K7jiM6t2wZW3ku6JM/bPbeSmUsRuayZyZa3+KBQRWaEUppeBy+2i7C6D4S8cZuzrJ6j6l3vUyuptyOctuo+NceSnPfS2TeANeNh+bT07b2ygRG+BF55s2h6BPvAF6D8EkSq4+U/g0k9AcG39UWTlLWae6mXq4S48xX4qP7WTQKP6R4uIrGQK08vEHfRS/tGtdqD+ynEqP7NLb9lepLmZNCeeGeDYk33Ex5JEYgH2vb+ZbfvrCIS17HfBSYzBi/8AB/8O4gNQ3grv+SvYdTf41t4fm7npNOPfNEm1TxLaUUHp+1tw6+daRGTFU5heRr7KMGUf2szYP77CxLdOUvahzXrr9pewLIuhM9Mce7yP9heHyWXz9mqFt7fQtLsCj0cdUgrO0HF47ovw8jchm4TmG+FX/yc03wTutfn9nDsxxsS3TmKl85Te3kr4smr9bhARKRAK08ssZJRR8q4NTP34DJOhdsK7KvE1FGuU+nVSsxlOPj/E8Wf6Ge2ZwRfwsOXqWrZfV095XZHT5cnFyqbg+Pfhhb+H7mfBG4Rdd8EVn4aqLU5X5xgrk2fqx6eZebYfX22Esg9txlelqUoiIoVEYdoBRdc2kB1NknhukMRzg+B24auLEGiM4l8fxb+uGE8ssOZauVmWRf+pSY4/00/HSyPkMnnKG4q49q5NGFfU4A/px7XgjHfCi/9o94eeHYPSJrj5s3DJRyFc5nR1jkr3xBm/3yQ7PEfR1XWUvKsJl29tjsyLiBQypRMHuFwuSu9oJfquDaR74qS7pkl3TZM4OMjMs/32B3nd+CqCeCtCeCvD89sQvqow7uDq+rbFx5OcfH6QE88MMDUyhz/oYfO+WrZeXUtlY7He7i402RS0PQiHvmp35XB5wHi3fUHhxhvW7FSOs6xsnunHuok/0YOn2E/FJ7YT3FTqdFkiIrJAqyuVFRhPxEdocxmhzfYInZWzyAwmSPfFyY7MkR2ZIzM4y9zxMcif97yoH29VGF9V+NWtryZcUBcrpeeytL80zMnnBuk7NQkW1LXGuPRXNtB8SRU+TXspLJYFA0fsZb5f/iYkJyFaD9f/kT0KHVV/dYB03wwT95tkBmcJ760m9p6NuPWOi4hIQdNv8RXE5XHhry/CX//aOcFWLk92PEl2eI7MyCzZoVkyI7MkXhjESp9L2e6oH191GF9NxL5Vh/FVR1bMW8e5bJ6eE+OYzw1y+sgouUyeksoQl7+niU2XV6utXSGaGYFj37KncQwdA08AtrwHdn8YNl4Pbv1RBPY5HP9ZD9M/7cEd8VH+sa2EtpQ7XZaIiCwChekC4PK48VWG8VWGCXHuBdjKW+SmU2SGZskOzpIZSpAZTDDz837IWvYHucFbGcZfG8FXV4SvNoKvNoKnyL8stedyefraJmh/cZjOwyOkZrMEIz62XlXLpitrqN4Q1TSOQpOK29M4Xv4mdD4OVg7q9sCvfB623wEhTVk4X6p7msnvtJMZTBDeU0XsvRsL6l0kERH5xRSmC5jL7cIbC+KNBcE4dzGXlbPIjs+RGbDDdaY/Qer0FLOHR179GE/Uj6+hGH99Eb750XBP8eIE7HwuT9/JSTtAHxohmcjgD3po2lVJy6VVrNtappZ2hSabho7H7ABt/hiyc1DSaK9QuPODa7ojx1vJJ7NMPXyGxIEBPMV+yj+yldA2jUaLiKw2CtOrkMvjenUkm52Vrx7PJTJ2wO6fId0/Q6ZvhuSJMZgfxPaUzAfsdfO3hmLcgQt7mz6TztFzfJzOwyOcOTpKKpHFF/CwYWcFrfMB2uvTW/4FJZuCjp/B8e9B248gNQWhMth9tx2g110BelfhDSzLIvnKGBPf7yAfT1O0r47oO9fjDujXrYjIaqTf7muIJ+LD0xIj2BJ79Vg+mbXDdd8M6d4ZMr1xkq+M2Q+6wFcdxr8uir+xGP/6KN7K0KvTMpIzGc4cG6Xz0Ag9x8fJZvIEwl427Khg4+5KGreV4dWFhIUlk7Q7cBz/nj0CnZq2l/Te/Cuw7X32AiseTVF4K9nJFJMPtJM8MY6vNkLFR7biX1fsdFkiIrKEFKbXOHfQS2BjjMDGcwE7l8jYLfvmb7PHRkkcHLQfDHpIRnwMz+boHpljImsRigXYclUtTXsqqWuNaQpHoZkdh5MPg/kgtP8UMgkIxmDLr9oBuuk68C7PHPtCZWVyxJ/sI/54DwAltzZRdHU9Lo9G7kVEVjuFaXmD81v2peey9LaN0//SMLOnJolMZShLZGn0uGgs8oLbhb+xiEB5gIDHhStngQajV77xTnvkue1H0P1z+yLC4lrYdac9Ct10nUagL4BlWcwdHWXqR6fJTaYI7aig5N1NeMuCTpcmIiLLRGFaXiOftxjpitN9fIyeE+MMdk5j5S18AQ/rtpRRuqOcxu3lBL1u0l3TpM5MkeqcIv54D/Gf9tjhuqHIHu1uKSGwvmTFtOZb0zJJ6HoaTj0Kpx6B8Q77eNU2uOZ3YfOtULtnzS+ocjHS/TNM/qCT9OkpeynwD256zTs8IiKyNihMr3GWZTExOEufOUHfyQl62yZIzWbBBZXritnzjkYat5RR01yCx/vaoBXaWk5oq92dIJ/Kkj4zTer0fLh+std+y9vrJrAhSmB+rravrmjNLZPuCMuCsQ7o/Bmc+gmcftLuwOENwob9cMWnoPUdUNbkdKUFJzedZvrRLhIHB3GHvMTe30Lkshr9XIuIrFEK02uMZVlMjczRf3KSXnOCPnOC2ek0AEWlAZp2VdC4tZyGzaWELqJVnjvgJWiUEZxv0ZdPZUmdnibVPkmqfYLph84wDbjDXjtYbyojaJQuWjs+ARKjdt/nzp9Bx+Mw3WsfL90Al3zEDs8brgFfyMEiC1c+mSX+RC8zT/dh5S2KrqojelOjekaLiKxxCtOrXD5vMdY3w0D7JP2nphhon3w1PIejfuqNUhqMUuqNGNGK0KItoOIOeF+zVHounibVMUny1CTJkxPMvTwKgK8u8mqw9jdGdcHWxZibgK5n4czTcPopGDpqHw+W2HOe9/8eNN8ApU1qYfc2WNk8MwcGiP+0m/xsltCuSkresR5vuf4oERERhelVJz2XZejMNIOdU/atY4p0MgfYI8/1Ril1rTHqWmOU1oSXbfVBT7Gf8O4qwrursCyLzECC5MkJkuY48Sd7iD/egytkB/DgljKCm0pxB/Xj+RqJMeg5YIfnM0/B4DHAsqduNFwGN/5H2HgD1O3WMt6LwMpbzB0ZYeqRM+QmUgRaYpS8awP+BrW6ExGRc5RWClg+bzExmGD4TJzB01MMdU4x1p94dRGW0toILZdVU9cSo7alhOgKGUlzuVz464rw1xURvX4d+WTWHrE+MUaybZzZQ8PgcRHYWEJoSznBreV4YwGny15elmV33Oh5zu620X0ARk/aj3mDsO5yuOHf2dM26veCd419fZaQlbeYOzrC9GPdZIfn8NVFKL29lWCrlkkXEZE3UpguEJZlMT2aZLhrmuEz0wx3xRnpjpNJ2aPO/pCXmqYoG/dUUbMxSvWGKIECmcvpDnoJ76ggvKMCK2+R7p5m7vg4yRNjTH6/A77fgX9dMaHtFYS2l6/Ot9dTM9B/CHoPQt+L0PM8JIbtx4IlsO5K2PUhaLxS4XmJWHmLuWOjTD/aTXZ4Fm91mLK7NxPaXqGLC0VE5C0pTK9A+bzF5OAsIz1xRnrijPbEGe2ZsbtsAB6vm4p1RWzeV0vVhmKq1kcprQ6vihd8l9tFYEMJgQ0lcGsTmZFZ5o6NMXdslKkfn2bqx6fx1UUI7aggtKMSX0UBButcBkba7PDc9yL0vgjDr4CVtx8va7bnOjdeCY37oMJQy7olZOXyzL0yZo9ED83irQpR9qHNhHYoRIuIyC+nML1C5PMWPSfGOfF0P12vjJFN28HK43VTXh+heW8VleuKqd4Qpawu8oY2dauVrzKM74Yw0RvWkR1PMnds1B49fLiL6Ye78DUUEd5VSXhnJZ6SFTham8vY0zMGjtjhuf8QDB6FbNJ+PFACDXth87+B+kvtUedIubM1rxHp/hlmXxxi9sgI+ZkM3soQZXcZhHZWKkSLiMgFW7YwbRhGCfA1IAr4gd8zTfPnhmFcCfwNkAUeMU3zs4ZhuIG/BXYBKeCTpmm2L1etyyk+nuTEswOceLafmfEUwSIfm/fVUt0UpXJdMbGasJbnnuctC1J8bQPF1zaQnUwxd3SE2cMjTD14mqkfnSbQVEJodyXh7RXOtCtLxWHoFTssDxyxt8MnIJeyH/cXQe1uuOyTULfHvpU2adR5GeXiaWYPjzD70hCZgQR4XIQ2lxHeW01wc5lCtIiIXLTlHJn+PeAx0zT/2jAMA/hn4BLgfwN3AJ3Ag4ZhXAJsAIKmae6bD9ufB25bxlqX3EhPnAPf66D7+DgA67aUcfUdrTTtrMCjFQN/KW8sQPH+Bor3N9hTQY7YwXryO+1MPtBBaGu5HZBaSxe/3Z5lwczQa0Pz4FH7gsGzV3+GyqB2p704Ss1Oe7+8VcF5GeVm0mQGEmT6E6QHZsj0J8iOzIIFvoYiYrc1E9pZiSdSGNcWiIjIyrScYfqvsEeZz/67ScMwokDANM0OAMMwHgZuAmqBhwBM0zxgGMaly1jnsnj8a21Mjya59NYNbNlXS7QQ5/6uEL7KML6b11N8UyOZvhlmDw0ze3iYuaOjuIt9hPdUEdlbja86cvGf/Ow0jcFjdh/nwWMwdAwSI+c+pnQD1OywLxCs2WEH5+Ja9XZeJlYmT2Z4lsxggsxQgsygvZ+f76cO4IkF8NVGCO+sILSzEl9V2MGKRURkNVmSMG0Yxq8Dv/u6w/eapnnQMIwa7Okev4M95WP6vI+JAxvnj0+ddzxnGIbXNM3sUtS73CaHZhnuinP1r7Ww++ZGp8tZNVwuF/6GYvwNxZS8u4mkOU7ixWFmnu5n5sk+fA1FRC6vIbyrCnfgdX2YLQumeuxpGa/eXoERE3Lzoczjh8rN9kqCNTvsEeea7Xa3DVlyViZPZmSW7MgsmaFZssPz29G5V98QwOPCVxUm2BzDVxfBV1uEvy6iVQpFRGTJLEmYNk3zy8CXX3/cMIwdwDeA3zdN84n5kenzV0AoBiaB8OuOu1dLkAZof3EIgJa9VQ5Xsnq5vG5C2yoIbasgN2PPk00cHGTyO+1M/bCDcFOaSHU7/vQRGDVhuA3S8XOfIFpvB+fmG6F6hx2ay1vAo1C2lCzLIj+TITsyR2bUDsrZkTmyw7Nkx5PnQrMLvOUhvFVhQjsq8NVE8NVE8JaHtIqmiIgsq+W8AHErcD9wp2maRwBM05w2DCNtGEYz9pzpdwKfBRqA9wLfnJ8zfXS56lwOp14YpralhKLSoNOlrF6z4zDWAWPteMbaKR5rpyjQTjroJpG+iYR5DQlzCz5vgKKKKOEde3HVGlC11Q7RoZjT/4NVy7Is8rNZsmNzZMeSdmA+uz8yizW/YicAXhfe8hC+uiJCu6vwVYXxVYft0KxrC0REZAVYzjnTfw4Egb+xrz9kyjTN24BPA18HPNjdPJ4zDOMgcIthGM8CLuDeZaxzSY31zTDen+DauzY5XUphsyw7MI932reJ0+f2xzthduzcx7o8ULoBV3kLgZZNBCqaiRUVkegrJ/FSiInBjUxNe4n4aom01uINrcAWewXGyubJTqbIjSfJzt9y43Ov7r8mMLvsOc3e8hDh3VV4K0L4KkN4K8N4YgF12BARkRVt2cL0fHB+s+MHgCtfdyyPHbJXnVMvDOFyQfMlmuLxS6XiMNkDk90w2QUTXTBx5tz++dMycEFJA5Q1web3QEWrPS2jvBVK179heoYbKN4ERddbpDqnmHm2n/gTPcSf7CG0vYKiq+vxNxbj0kWEbyqfzJKbStmBeTJFbiJFdiJJbiJJdjJFPp4+NyUDwOPCWxbEWxbE3xi1p2iUB/FWhPCWBXGtkb7pIiKy+mjRlmVkWRanXhimYXMp4ajf6XKclc9BfBCm+2G6F6b67AsAJ3tgqtveJidf+xxfGGLr7XC84Rp7v7zZ7tVcun5BS2y7XC6CzTGCzTGy40lmDvSTeH6IuZdH8dUXUby/ntCOyjUzD9eyLKxkjtx0itxUmtxUitz0/Hb+lp1MvXZkGcDtskeXYwGCraV4SwN4YnZ49pQH8RT7NcIsIiKrksL0MhrpjjM9Msfed613upSllU7YQTk+ANMDEO+f387fpvrsrfW6QOYvgpJ1EFsHDZfb25J18wF6A0QqlrTdnLcsSOzWjURvXs/sS8PMPNPH+DdMPA+foXh/A+FLq3H7Pb/8E61AVt4iP5clH0+Ti6fJzWTIT8/vT9uBOR9Pk5tOY2Xyb3i+O+LDU+LHUxbC31SCNxbAEwvgKZnfRjUdQ0RE1iaF6WV06uAQbo+LjbsrnS7l4uVz9jzkmSGYGbb7LM8M2/fjg6/dpqbf+HxfBKK1dv/lpv0QrbM7ZpQ0zG/rIRhbEb2Z3X4PRVfWErm8hmTbOPEnepn8fgfTj3ZRdFUdkX11K2KhDyuTI5fIkk9kyCcy5GbS5GcydlCeSc8fy9gheSYDeesNn8Pld+OJBnAX+/E1FBMs9uOJ+u2QXOLHEw3gifo1DUNEROQtKEwvEytv0f7iMI3bygmugCBGPgdzE3ZAToza29kxmB217ydG5m/z+7NjYL1xxBJvCIqroagGqrdBy01QVA3FNXZwjtbZ20DxigjKF8PldhHaWk5oazmpM1PEn+hl+tFu4k/0EtxSRnBTKcFNZXje5pQdy7Kw0jnys1n7NpeZ38+QT8xvZ7PkEpn5Y/bNSr/J9wPA48JT5Mdd7MNT5MNXGzl3v9j/mn13UL8CRERE3g69ki6Tgc4pZiZS7Ht/8+J+4nzOHgmem4C5yfntxOvuj9udL87fzk3y2ivEzhMosadURCqhbCOsu9zeL6o+ty2qsvcLMCQvRGBDCYENJWSGEsw808/ciXHmXh4FwFcbIWiUEtxUiicaIJ/M2re5HFYya0+vOLudy2LNndvPz9kB+s1Gjc9yBTy4w17cER/usA9fZdi+X+Szp19E7K27yI+nyIcr4NGFkyIiIstEYXqZtB8cwutzs2FnxWsfyCTtrhWpaUhOzW+nz23PP5actO+f3c7NP/ZWoRjsecihUvsWLrPnIIfLIFz+2luk4tz+Ai7kWyt81RFKb28lZllkBhIkT06QOjlB/Mk+4o/3vvUTXeAOeXGFvLiDXtwhL76SAO6QF3fYZ4fjkHd+O39//rimWIiIiKxcCtNvl2VBesYOxMmp827nwm8+MUn7z69ifXgQ/6gAAAmqSURBVEk//vv+Yn56xbj9+Nmlqn8Rf5G9ZHUgai8mEm2Aqm32frDEnmscKrXvnw3OoVL7uHeNdw1ZIi6XC39dEf66Irh+HflkllTnFPlk9tWw7Ap6cYc8uINeXH6PLtATERFZhRSmL0Y+B9/+JIyY9ohwatoO0W82l/g8fbnLmEvfSGvkeXB7oWKTPTp8NiAHS+zpEoEoBKP2frDk3OPuwuwgsZa4g15CW8udLkNERESWmcL0xXC57V7HpRvmQ+954fdsKD47UvzqfpRT/9yJb3qY9f/6i1CgrdVERERE5I0Upi+GywXv+8JFPSWXzdN5aISm3RV4FaRFREREVhVd2bTEeo6Pk5rN0npptdOliIiIiMgiU5heYqdeGCIQ9rJuS5nTpYiIiIjIIlOYXkLpZJbOI6M0X1KFR+3NRERERFYdJbwl1Hl4hGwqh3FljdOliIiIiMgSUJheQuaBQaIVQWqbS5wuRURERESWgML0EomPJ+k1JzCuqNHSziIiIiKrlML0Ejn5/CBYYFxZ63QpIiIiIrJEFKaXgGVZmAcGqW0poaQy5HQ5IiIiIrJEFKaXwEh3nInBWYwrdOGhiIiIyGqmML0E2g4M4vG6adlb5XQpIiIiIrKEFKYXWS6b59TBIZp2VRAI+5wuR0RERESWkML0Iut+ZYzkTEa9pUVERETWAIXpRWYeGCRU7KNxq5YPFxEREVntFKYXUTKR4fTRUTZdXoPboy+tiIiIyGqnxLeI2l8YIp+1NMVDREREZI1QmF5EbQcGKa+PUNFQ5HQpIiIiIrIMFKYXyeTQLEOnpzGuqNXy4SIiIiJrhML0IjGfG8Tlgk2XVztdioiIiIgsE4XpRWDl7eXD120pIxILOF2OiIiIiCwThelF0NM2Tnw8yearap0uRURERESWkcL0Ijj+dD/BiI+NuyqdLkVERERElpHC9Ns0O53m9JFRjCtr8Pj05RQRERFZS5T+3qa2AwPkcxZbr6lzuhQRERERWWYK02+DZVmceGaA2uYSymojTpcjIiIiIstMYfpt6D81yeTQrEalRURERNYohem34fjT/fhDXpr3VjldioiIiIg4QGF6gZKJDB0vjbDp8mp8fo/T5YiIiIiIAxSmF8h8bpBcNq8pHiIiIiJrmML0AliWxfGn+6laX0zlumKnyxERERERhyhML8DQ6WnG+xMalRYRERFZ4xSmF+D40/14/W5aL612uhQRERERcZDC9EVKz2U59cIQrZdW4w95nS5HRERERBykMH2RTh4cIpvWhYciIiIiojB90Y4/3U9ZXYTqpqjTpYiIiIiIwxSmL0Iul2e0d4Yd1zfgcrmcLkdEREREHKZJvxfB43Fz7+euJlTsd7oUEREREVkBNDJ9kRSkRUREROQshWkRERERkQVSmBYRERERWSCFaRERERGRBVKYFhERERFZIIVpEREREZEFUpgWEREREVkghWkRERERkQVSmBYRERERWSCFaRERERGRBVKYFhERERFZIIVpEREREZEFUpgWEREREVkghWkRERERkQVSmBYRERERWSCFaRERERGRBVKYFhERERFZIK/TBSyQB2BwcNDpOkRERERkFTsvb3re7PFCDdO1AB/+8IedrkNERERE1oZaoOP1Bws1TB8E9gMDQM7hWkRERERk9fJgB+mDb/agy7Ks5S1HRERERGSV0AWIIiIiIiILpDAtIiIiIrJACtMiIiIiIgtUqBcgrjiGYdwEfAwIA//ZNM0jDpcksqIZhnEjcLdpmp90uhaRlcQwjKuAT83f/VemaU46WY/ISrYSXks0Mr14wthh+r8A73C4FpEVzTCMFuASIOh0LSIr0G9gh+kvA3c6XIvIirVSXks0Mr1AhmH8DnDz/N2fm6b5XwzDiAC/Dfyhc5WJrDxvdr4Af2kYxtccLEtkpfKYppk0DGMAuNHpYkRWKtM021kBryUK0wtkmuZfA3999r5hGOXA54A/Nk1z2LHCRFag158vIvILzRqGEcDua6ulfkVWOIXpN2EYxhXA50zTvN4wDDfwt8AuIAV8cv4vodf7K6AS+HPDML5nmua3lq9iEecs8HwRWZMu8Hz5P8CXAB/n5k6LrCmF9NqiMP06hmH8AfARIDF/6H1A0DTNfYZhXAl8Hrjt9c8zTfOjy1elyMqw0PPlLNM071n6KkVWhgs9X0zTfBH4uDNVijjvYl9bnH4t0QWIb9QB3H7e/WuAhwBM0zwAXOpEUSIrlM4XkQun80XkwhTUuaIw/TqmaX4byJx3KApMnXc/ZxiGRvRF0PkicjF0vohcmEI7VxSmf7lpoPi8+27TNLNOFSOywul8EblwOl9ELsyKPlcUpn+5Z4BbAebn6Rx1thyRFU3ni8iF0/kicmFW9LmyYobIV7DvArcYhvEs4ALudbgekZVM54vIhdP5InJhVvS54rIsy+kaREREREQKkqZ5iIiIiIgskMK0iIiIiMgCKUyLiIiIiCyQwrSIiIiIyAIpTIuIiIiILJDCtIiIiIjIAilMi4iIiIgskMK0iIiIiMgCKUyLiIiIiCyQwrSIiABgGMYOwzC6DMP4jNO1iIgUCoVpEZECZBjG9YZhfONtfo5ywzC+dPa+aZpHgbuAj84/XmMYxv96e5WKiKxuCtMiImvXnwFfeN2xYWAbgGmag0DcMIzrlrswEZFC4XW6ABERWRyGYfiAvweaAQ/w303T/H+GYYSArwB1QA9wLbAZuMw0zddP6fgLIGAYxnrTNLuA+4DPAk8s039DRKSgaGRaRGT1+BQwaprmVcDNwJ8ZhlEB/AZw2jTNq4E/AaqBKwHz/CcbhvEuIAI8yPzoNHAcuHpZqhcRKUAK0yIiq8cW4EkA0zTj2EG4ef74s/PH24ARoAIYOvtEwzCCwH8FfhM4Cmyf//gckDUMQ68XIiJvQr8cRURWjxPAfgDDMIqBHcBp4Biwb/54M3aQHgZi5z33PwBfMU3zDOeFacMwXEDWNM388vwXREQKi+ZMi4gUrncYhvHCeffvBv69YRhPAyHgs6ZpDhuG8WXgHw3DeBLoApLAAeBzAIZhGMAtnJvOcRT4d/P7O4CfL/n/RESkQLksy3K6BhERWUKGYVwFFJmm+YhhGK3AQ6ZpNhuG8b+BL5mmeegXPPe/Aj8wTfOp5apXRKSQaJqHiMjq1wn8kWEYzwBfB35r/vgfY8+RflOGYdQAUQVpEZG3ppFpEREREZEF0si0iIiIiMgCKUyLiIiIiCyQwrSIiIiIyAIpTIuIiIiILJDCtIiIiIjIAilMi4iIiIgskMK0iIiIiMgC/X97RhlylMxVmQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (12,8))\n",
    "for i in range(10):\n",
    "    plt.plot(alphas, coefs_my[:,i], label = diabetes.feature_names[i])\n",
    "\n",
    "plt.xscale('log')\n",
    "plt.xlabel('Log($\\\\lambda$)')\n",
    "plt.ylabel('coefficients')\n",
    "plt.title('Lasso paths - Sklearn')\n",
    "plt.legend()\n",
    "plt.axis('tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.007079457843841388, 14.12537544622754, -354.404849586707, 616.6707029880628)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (12,8))\n",
    "for i in range(10):\n",
    "    plt.plot(alphas, coefs_lib[:,i], label = diabetes.feature_names[i])\n",
    "\n",
    "plt.xscale('log')\n",
    "plt.xlabel('Log($\\\\lambda$)')\n",
    "plt.ylabel('coefficients')\n",
    "plt.title('Lasso paths - Sklearn')\n",
    "plt.legend()\n",
    "plt.axis('tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. 参考\n",
    "- https://www.cs.cmu.edu/~ggordon/10725-F12/slides/25-coord-desc.pdf (coord-desc.pdf)\n",
    "- 对绝对值函数求导用到了次导数的概念 https://en.wikipedia.org/wiki/Subderivative"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. 调整\n",
    "- 主要是调整了$X_{-q}w_{-q}$的实现"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "w = np.random.rand(*X[0].shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "24.9 µs ± 3.7 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n"
     ]
    }
   ],
   "source": [
    "index = [i for i in range(len(w)) if i!=5]\n",
    "%timeit X[:, index].dot(w[index])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.49 µs ± 840 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n"
     ]
    }
   ],
   "source": [
    "w[5] = 0\n",
    "%timeit X.dot(w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "language": "python",
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  "language_info": {
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    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.1"
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  "toc": {
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